I have the exact same problem. It's nice to know I'm not alone. I've been scared to mention my fears on lesswrong because I didn't think anyone would understand.

I'm mainly concerned about many worlds interpretation being true. I don't take dust theory seriously. Unless I understand it wrongly, it removes causation and just assumes the information itself is what is important. I really recommend you read Causal Universes. It's one of my favorite Lesswrong posts.

I also think dust theory leads to absurd and obviously wrong conclusions. Like how do interpret some random collection of bits? Under different interpretations they can represent anything.

If it's true that causation doesn't matter, then it's really weird that I just happen to find myself here with memories of living in a causal universe with simple, universal laws, for the last 2 decades. I should expect to be a boltzman brain observing extremely high entropy.

Anyway, my main tactic of dealing with Scary Idea is just keeping my mind off it as much as possible. Thinking about it hurts me, so I don't think about it. I also think I've resolved it somewhat, but again I prefer not to think about the issue at all.

I'm really scared of the transhumanist future. If we massively increase our intelligence, or create AIs which can explain complex ideas to us, then we will be forced to deal with all of these existential issues all at once. Including ones we haven't even thought of yet or can't understand. Our simple minds allow us some cognitive dissonance to just ignore this stuff.

EDIT: Also lighting helps a lot. I feel much worse in a dark room than a bright one. During the day time in the sunlight my mood improves even more. So I can understand why these problems occur during bedtime. Reading until I fall asleep helps. During the day I just find things to keep my mind off of it. If I started getting really terrified, I just opened a reddit page and looked at cat pictures for awhile.