I can sympathise. I live in social housing and the walls are very very thin. I have misophonia and my psychiatrist think I'm on the autism spectrum, but I've never had the full adult autistic test so I can't say I am autistic iyswim.
There's a constant state of alertness I live in, forever trying to ignore the sounds from next door but in trying to ignore them, it becomes even more noticeable.
Even when they're silent, my ears are still attuned and just waiting for the next bang, this, scream, door slam, dog bark etc.
People that don't know what it's like, maybe don't appreciate the rattling of nerves that comes with the near constant barrage.
Imagine, if you will, when ever you're sat quietly, someone let's an air horn off... Then tells you they'll be letting air horns off several times a day, you won't know when, but it's coming.
That might give a sense of what it's like.. for me anyway.. op sounds similar.
In saying all that, and after a great deal of mental health help, I've come to the conclusion that it's better for me to manage my exposure and reaction than to move house or try to control others.
So, lots of walks out onto the peace of the country, earbuds connected to TV, earbuds & white noise for sleeping, windows constantly open for ambient noise of traffic and wind etc.
The most helpful has been the earbuds. I buy specific ones by Panasonic called ErgoFit, they're shaped to fill the ear canal so they keep noise out like earplugs, they're relatively cheap and comfortable. (Probably wouldn't win any awards from audiophiles mind you)
Ultimately though, what you really need to consider is your quality of life... If it really isn't of.much quality, and moving would help, well.. you got your answer. You could always ask your landlord or local social landlords etc if they've a property.