I know of what you speak! My solution may not work for you, but here's what I did:
First, identify all the really important things, and make sure they get done. For me, this meant either making them part of my core routine, or making a list. 'Core routine' means a required set of actions; if it is necessary to walk the dog or he will pee on the carpet, I walk the dog as soon as I get home - before sitting down, before logging into my computer. I don't do anything else until my routine is completed.
Likewise, I make the list of need to do as central to my life as it needs to be to in order to get it done. If I must pay the rent tomorrow, the note to pay the rent is on top of my computer, and I cannot compute until it is done. If that is not sufficient, tape the note over the door handle, and don't leave the house until you have payed the rent. My list is rarely more than three items long -- there's just not that many things that are really important any given day. (If an electronic list is more useful than a physical one, simply make checking your list part of your core routine; check it before you head out the door every day).
Once the big stuff is out of the way, actually do stop worrying. The dishes are not important, so if you suddenly think of an interesting idea that you want to write down, walk away from the sink and do it. If you get distracted by 20 other things before you get back to the sink, so what? You may need to spend a couple days practicing this -- instead of just thinking "oh, I should write that down", drop what you are doing and write it, not because the writing has priority, but because you are practicing being less stressed about completing/switching tasks.
It didn't take me long practicing this before I started getting more organized in planning the unimportant tasks without much stress. Once I knew that the important things were taken care of, and once I got serious about not caring that the trash was taken out right now, I felt less stress over all, felt less rushed, and took the time to plan things out just enough that I was was able to organize things efficiently.
If you're capable of having routines, you don't have this problem as badly as some people do.
This thread is for asking the rationalist community for practical advice. It's inspired by the stupid questions series, but with an explicit focus on instrumental rationality.
Questions ranging from easy ("this is probably trivial for half the people on this site") to hard ("maybe someone here has a good answer, but probably not") are welcome. However, please stick to problems that you actually face or anticipate facing soon, not hypotheticals.
As with the stupid questions thread, don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better, and please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
(See also the Boring Advice Repository)