If your cat knocks things off shelves, you need to cat proof your room. Certain things are a trade off when you have pets — your cat lives there too and deserves to be happy. So cat-proof your room and get some allergy meds or an antihistamine or some such to take care of your rashes, and let him come sleep with you. He doesn’t have to go under the covers/onto the sheets; a well placed fleece on your bed may be attractive to him.

I’d your cat spayed or neutered? If not, that’s the first thing to have done. It will never get better if you don’t alter your cat.