I suspect that if somebody had given me this advice when I was a student I would have disregarded it, but, well, this is why wisdom is notoriously impossible to communicate. Wisdom always either sounds glib, banal or irrelevant. Oh well:

Anxiety, aversion and stress diminish with exposure and repetition. 

This is something that, the older I get, the more I wish I had had this tattooed onto my body as a teenager. This is true of not only doing the dishes and laundry, but also vigorous exercise, talking to strangers, changing baby diapers, public speaking in front of crowds, having difficult conversations, and tackling unfamiliar subject matters. All of these are things that always suck, for everyone, the first time, or the first several times. I used to distinctly hate doing all of these things, and to experience a strong aversion to doing them, and to avoid doing them until circumstances forced me. Now they are all things I don't mind doing at all.

There may be "tricks" for metabolizing the anxiety of something like public speaking, but you ultimately don't need tricks. You just need to keep doing the thing until you get used to it. One day you wake up and realize that it's no longer a big deal.

What you really wanted from this answer was something that you could do today to help with your anxiety. The answer, then, is that if you really believe the (true) claim that simply doing the reps will make the anxiety go away, then the meta-anxiety you're feeling now (which is in some sense anxiety about future anxiety) will go away.

My personal approach is to do something you like but have no time for otherwise that can be done at the same time as the chores. I listen to podcasts or audiobooks while doing dishes, for example. My framing is "without chores, I'd never have time for this fun stuff".

I do have this feeling from time to time. Some stuff that's helped me:

• Simplify, simplify, simplify. Do your chores with as little effort as possible, per https://mindingourway.com/half-assing-it-with-everything-youve-got/. Buy stuff that does your work for you. Your goal is to complete your chores, not to do work; work is in service to the goal, not the goal itself.
• Success by default. Make the easiest, lowest-energy, laziest way to do the thing also the right way. Have exactly one clothes hamper for dirty clothes. Buy clothes that don't need ironing. Put decorative items on unused surfaces so you don't put random junk on them.
• Suggested to me by ACX commenters: random rewards. Pick something you like (chocolates, kisses from your wife, etc.) and set up a timer that goes off at a randomly selected interval which entitles you to that reward. The randomness might help your brain to associate chores with better feelings.
• Make it satisfying: Power-washers for big jobs, steam cleaners, compressed air, powered dish brushes. There's a lot of cleaning content on /r/oddlysatisfying for a reason.

This next one's a lot more speculative, feel free to completely disregard. Seriously, I'm suggesting the following because it works for me, but my anxiety response might be way less than yours is and my method might be totally useless for that.

Anyway, it sounds like you have a strong anxiety response when either doing chores or thinking about them. I had a similar issue, and my strategy was flooding, exposure therapy turned up to eleven. Do not recommend.

My real suggestion is, when you feel these racing thoughts and fast breathing, is to stop the chore for a moment and stand there. Don't try to distract yourself, because the focus is, for a moment, now on the anxiety response itself.

For me, anxiety is a series of waves of intense physical symptoms like fast heartbeat and breathlessness. There's definitely a sense of "here it comes!" before each next wave. One thing that helped me was realizing that, while the anxiety response can be quite long-lived, each wave was only 10-15 seconds long. Noticing this gave me strength; if I make it through this wave, I'll have a few minutes to work with the anxiety before the next. This may not be true for you, though.

You say that the endless nature of these chores terrifies you. In this moment of standing still, your goal is to dig a bit deeper, to try to ask "why does the fact that these chores are endless scare me so much?"

Possible answers could be:

• Endless chores scare me because they'll take up a huge chunk of my finite life.
• Endless chores scare me because every time I finish them, I have to do them again soon; all my previous work has amounted to nothing.
• Endless chores scare me because my thoughts race and my breathing speeds up.

Or something else entirely! It might take awhile to get a good answer, and you might have to think through many of them until one seems to fit.

All this might sound very familiar; you say you're taking anxiety medication, but you may also have heard all this through therapy (Cognitive Behavioral Therapy) or meditation. Again, my advice works for me but may not work for you! Please don't feel bad if this doesn't apply!

Regarding a drug-based solution, I recommend Silexan. Scott Alexander wrote about this not that long ago on ACX, and anecdotally, it's been shockingly effective for anxiety issues that arose for me a year ago.

Regarding an entirely psychological, but still clinical solution? Consider starting online therapy with a psychologist/psychiatrist. This has helped me as well- not to the same extent as the Silexan, I think, but it still helped just because it was a dedicated hour per week of thinking about it and voicing those thoughts to someone. Almost every breakthrough came from me just rationally talking it out, but that was 10 times easier in therapy than on my own because I had nothing else to get distracted by or be doing during that period. That, and talking about one's problems to another party has been proven to improve problem-solving effectiveness as compared to thinking them through internally, even if the other party is doing nothing but listening (or even if they're a literal inanimate object like a rubber ducky).

Finally, for my own anecdotal "folk" solution that I completely made up, but which helped me at one point and might be helpful to you as well: try to imagine two selves inside of you in a dialogue, one of them completely calm and rational, and the other embodying whatever your emotions and impulsive thoughts are (so during a panic attack, this would mean picturing one of you who's having the panic attack and another who's calmly thinking about what to do next to resolve the situation). Then, in the dialogue, picture the rational one consoling the emotional one (which is a perfectly rational thing to do for someone who's stressed or anxious).

That last one, I used for a week or two with moderate effectiveness, and then I transitioned from that to standard self-compassion. I'd heard about self-compassion before, but I didn't really get how to actually do it until I'd gotten some practice with that toy model of the rational and emotional selves.

Consider seeing a doctor about the panicky and stressed feelings. They may test you for hormone imbalances or prescribe you antianxiety medication.

I have a similar problem. What worked best for me was simply removing chores from my life.

I realised I was mentally comparing myself to an unrealistic standard of chore-completing perfection (brushing and flossing three times a day, showering/bathing daily, cleaning my apartment every night, doing the dishes after every meal) and feeling perpetually guilty for being a poor adult when I failed to meet my own demands. I realised that leaving an apartment somewhat untidy until I was expecting company was completely fine, that bathing every other day was quite enough hygiene-wise, started using paper plates and plastic cutlery so I wouldn't have to do the dishes ever again (this alone was the greatest relief), etc. So, my suggestion would be to go through your chore list, and see which are being imposed on you by social convention and eliminate as many as possible. Be rationally lazy. Make life work for you. Half-ass it with everything you've got.

The tasks you are talking about are known in caretaking and occupational therapy as Instrumental Activities of Daily Living. Many people do find them difficult to manage independently.

Seeking out occupational therapy may be helpful. Interventions you might pursue with or without their help include skills training (practicing the task to gain confidence with it, or learning easier ways to do the task), modifying your living environment and making use of tools that help you carry them out with less friction, and looking further into training cognitive skills that help with the task. You might also consider screening for any psychiatric conditions that may make this an additional challenge and look into any useful treatments or management associated with anything you find.

I got a lot of value out of How to Manage Your Home Without Losing Your Mind: https://www.aslobcomesclean.com/book/

The high level takeaway is that these tasks become much more manageable when you establish a consistent set of habits and routines around them. There's a lot of very specific step by step advice for creating those habits. It's still the same amount of work, but feels less overwhelming once you have a grasp on how much work it actually is and experience with each task.

Not a complete answer, but something that helps me, that hasn't been mentioned often, is letting yourself do the task incompletely.

I don't have to fold all the laundry, I can just fold one or three things.  I don't have to wash all the dishes, I can just wash one more than I actually need to eat right now.  I don't have to pick up all the trash laying around, just gather a couple things into an empty bag of chips.

It doesn't mean anything, I'm not committing to anything, I'm just doing one meaningless thing.  And I find that helps.

Some things that help me:

• Having a proper task tracking system with due dates (I use rememberthemilk but it's not necessarily the best one, just what I'm used to.) Once you know that all your tasks are accounted for, you don't need to stress about forgetting something. You should be "stateless", your brain occupied by whatever you are doing at the moment, and not by fretting about all the other stuff you need to do. (stolen from getting things done.)
• Have a dedicated "chores day" once a week when you do all the chores that (i) don't need to be done more frequently and (ii) don't have any other specific time they need to be done. You implement it by assigning every new chore to the next chores day in your task tracker. If, during chores day, you don't finish all of the chores, then move those that suffer delay to next week and the urgent ones to tomorrow. This system makes all non-chore-days both more relaxed and more productive.

The perspective in this post has been quite helpful to me for dealing with this and might work as a new thought paradigm if viewing these things as obligations is part of what is causing your stress. If the never-ending nature of the tasks itself is an issue, then perhaps this post can help with that. 

Something I've found helpful for similar issues is to change my mindset from "I need to x" or (worse) "I should do x" to "I want to do x", even if the reason is because the consequences of not doing it seem very bad. Trying hard to reframe things as a desire of mine, rather than an obligation has been very good for me (when I can do it, which is not always).

Wow I just saw this on the frontpage and thought I sometimes feel like this too, although about slightly different things and without that much heart-racing. I'm late and there are already many good answers, but here are my extreme and possibly horrible lifehacks for when I'm struggling/feeling lazy during the pandemic:

tldr: Like others said, get away with less chores. 

I haven't ironed or folded clothes since like forever. (If you really cares about that, maybe find clothes that look OK without ironing, idk). I don't go out or exert myself that much, don't change clothes that often if I don't want to, and bought plenty of similar clothes (online, in bulk or used) so I can let laundry pile up more and do more at a time (assuming I can use a washing machine; if you don't have one or can't easily access - say the laundromat is too far from your home, there are other tricks for hand washing).  Maybe unethical tip: most people don't need to shower that often either(just be less self-conscious unless someone important in your life minds it) and can use dry shampoo(or body powder/corn starch), alcohol and wet wiping etc to delay the need of showering and shampooing, in case these tasks are unappealing to you; also silk clothes are known to absorb oil from the skin better and can last longer before having to be cleaned - you can get lots of used silk shirts for cheap, and they are comfortable too if you have sensory issues or hate static.

I rarely need to "do dishes" as I cook for myself and can take shortcuts/lower standards. You could use disposable plastic cutlery and paper dishes, but I don't like them. Instead I use quality nonstick pots and pans (imo important!) that just need a gentle wipe, and 1-2 microwave-safe containers if necessary, and either cook one-pot meals, or batch cook things like stews(or order family-sized delivery for savings, if it's something I like and can't easily cook myself) and portion and freeze them to be reheated on the plate in a microwave or added to the pot. You can cook starch(like rice/pasta) and veggies and add seasoned raw protein or frozen stuff on top, in a pot (or Instant Pot, or a large ceramic bowl in the microwave), so no need to wash separate containers. If rinsing just 1 pot and 1 bowl/plate per meal is too much or if you can't rinse immediately after the meal, you can just wipe the pot with a paper towel (with a bit of water if you must), and store used plates in a separate plastic bin (not in the sink itself) and soak/wash them in a batch, without making the sink unusable for other tasks.

Like others said, most other chores can be simplified or automated (like robot vacuum or rearranging storage so things are dropped at appropriate places more naturally), or at least you can get away with doing less. Dust build-up can be reduced by air purifier (especially one that's next to the window, and it's good for you too), and most people don't really need to wipe most surfaces that often. The only time I really need to make my bed is after changing sheets. You didn't mention storage/organizing, but I struggled a lot with it. YMMV because storage needs and habits vary wildly. Some are just minimalist and will never want to have all that stuff I keep. Some prefer drawers so they don't have to see the stuff. I prefer (large, metal) shelves/racks and other open storage, and open boxes/bins organized by category (OK, mostly) on top of that, so I can maximize the amount of stuff stored for the amount of visual clutter while keeping things easy to access and put back(important imo, if it's not easy I might as well not have the item/storage).

I can't say much about food shopping as tastes and environments are different, and I personally don't mind shopping that much, but having a list of favorites/repeated purchases (especially for online shopping), ordering larger amounts and batch cooking (and/or freezing) may help. If cooking larger batches seem difficult, maybe choose ingredients that need less preprocessing (like veggies that need less/no peeling), and an Instant Pot and/or hotplate/electric griddle with digital temperature controls can help take out the skill/guess factor. Canned/non-perishable goods are helpful too. Just be careful about nutrients like protein and fiber if you decide to make changes to your diet for convenience; also you can freeze almost anything - frozen fruits/veggies are great and better than sad refrigerated leftovers imo.

As for having to work, I'm sorry but I don't have better ideas other than choosing a job/environment that suits you more, ideally one that is fun and meaningful to you so it doesn't feel like it's taking time away from your life that could be spent doing more meaningful things, or at least one that is not unpleasant and leaves you plenty of time and energy to do other things you like. And be sure to have fun and avoid burnout no matter how meaningful your career/cause is.

If there are too many such tasks, maybe its time to find a way of life which removes most of them:

• Hire a cleaner
• Order food from restaurants or eat outside. 

There's a cluster of things around non-coercion, parts work, and coherence that might be helpful here.

It could be good to start with something like focusing, which can help you find the meaning behind the stress, and may give you more information about how to address it moving forward.

Maybe a shit answer but becoming great at meditation allows you to be with emotions without trouble. Chores then become an oppurtunity to deepen your awareness and practice (more long term but you cut the root of the tree)

Not a doctor, but have you explored whether neurodiversity is part of the picture? What you're describing sounds similar to how adults with PDA describe their experience. 

Another helpful route might be to practice self-acceptance and stop blaming yourself for not being 'naturally' geared towards doing laundry. Once you do this you can focus on ways of solving the issue, e.g. paying someone to do the things you find hard. 

Something I find useful for chores is making rules, not individual decisions. (I daresay there’s a connection with TDT, although I learned this before TDT was ever invented.) For example, “all dishes will be washed before I leave the house or go to bed at night”.

You could be hypothyroid. What's your morning body temperature?

I've had the exact same experience. Chores like that are the exact kind of thing your brain says "nope" to (forcefully) when you don't have enough energy available. I've had this symptom for most of my life, and it's gone away during the times I've been healthiest. 

This - small chores seeming entirely awful - was positively correlated with all my other symptoms: insomina, depression, acne, brain fog, idopathic fatigue, and breathlessness under exertion (much more than normal). They all arrive and abate together, indicating they're all the result of an underlying root cause, and it's probably low energy availability, since my body temp has been 96.5 for most of my life.

That's my current hypothesis anyway, and the QOL improvements getting up to ~97.4 have been tremendous, so I'm sticking with it.

Maintenance - the process of preserving a condition or situation or the state of being preserved.

I call these things you refer to “Maintenance jobs”

I think that the answer you are looking for is in the definition of maintenance

• They are a trade-off for the things you enjoy

∴ you must do them to enjoy the things they generate

OR

∴ you don't have to accept the trade-off if you don't enjoy the result as much as you hate the maintenance.

In other words:

Life has a cost, and you must pay it.

Nobody said you had to enjoy paying it.

There's joy to be had in projects to reduce maintenance jobs

I quite love finding ways to reduce my maintenance burden, for example:

• Washing machine (look up the unholy task on manually washing your clothing, then worship your washing machine)
• Dishwashers (I calculated a ~4000% ROI per year)
• Clothes Dryers (much lower ROI, still positive depends on your time value)
• Robot vacuum cleaner plus no carpet (very little time spent vacuuming)
• Learning to cook efficiently (Could write a book, but consider time spent vs happiness vs $ cost) 
  • Egg, spinach and cheese pie (bought pastry sheets) (10 - 15 minutes prep = lunch for four days)
  • Rice cooker rice plus chicken tenders plus frozen veggies plus sauce (10 minute dinner)
  • Rice medley - 1 cup brown rice + 0.5 cups lentils simmer for 40 minutes add a can of beans, mix, portion, add grated cheese, sriracha and soy sauce. Heat in the microwave - yum snack.
  • Honestly baking cakes and cookies is easy as
• Replace your lawn with whatever you can get away with (I’m re-wilding honest)
• Design your garden for low maintenance wherever you can
• Live closer to work
• Biking is the most cost-efficient transport method (I hear cars may be needed in America)
• Replace hard to maintain things with easy to maintain things
  • I will not buy a shirt i have to iron
  • I will not buy kitchen things I cannot dishwash (except cast iron pans, worth in that case)
• I believe the FIRE movement had a bunch to say on jobs, minimalism has some good points, permaculture has some great ideas (kinda process optimisation for non-engineers)

Have fun finding better ways to beat back the menace of entropy!

Cognitive behavioral therapy for what appears to be fairly severe underlying anxiety?

Rebt in particular might apply as you seem to overwhelm yourself with the thought of the thing more than the thing.

Undiagnosed ADD comes to mind as "existential crisis doing chores" comes up a lot to describe it when I talk to adults.

Unified mindfulness would also be a suggestion, you can use the opportunity of the hated chores to wire up a more peaceful sensory experience and relationship to your body and mind.

Once you reach a certain age, you may find that these little tasks and chores become therapeutic. They offer a chance to step away from your desk and do something with your body. This isn't really a big deal in your teens and 20s, when your body can take all sorts of punishment and keep going, but once you pass the 30 mark, you may find that a little light exercise and movement feels really good if you've been sitting at a desk or staring at a screen all day.

Also, studies have shown that exercise actually improves mental acuity. I don't remember the exact details, but I recall one study that split students into two groups: one that studied for about 1 hour, and one that studied for about 45 minutes and exercised for 15. The second group (the one that studied less and exercised more) actually performed better on academic and memory tests.

So my advice is: don't think of chores as wasted time, but as opportunities to recharge your mind and body and actually accelerate your mental acuity. You might not think of folding laundry as exercise, but compared to sitting at a desk, it is.