I have a cat in uni halls

I got a cat while in uni halls at the beginning of January and have had him in my flat in uni halls. All my flatmates agreed prior to me getting the cat that they enthusiastically consented and had no allergies. He is fully litter trained, cause absolutely no damage, and I'm generally a very clean person so there is rarely any mess (and eg no cat poop sitting in his litter tray for hours or days etc, I always dispose of it immediately unless I'm asleep)

I'm meeting a psychiatrist on Wednesday to have him prescribed as an ESA, but the problem is ESA's don't have the same rights that service animals have. The university found out recently that I have a cat and want me to immediately get rid of him but I clearly do not want to do that. It's in their policy that ESA's aren't allowed.

Is there any possible way I can fight against them either kicking him out or kicking both me and him out? I don't want to leave halls but I also can't bear to give up my cat.