i dont think youre the asshole, but i do understand your roommate. my mon is also really allergic to cats, enough so that if shes in a room where a cat has one been (even if its been months and the room has been cleaned) her throat will start to close. While it's unlikely your roommate's mom will be staying over (at least i hope) your roommate could be worried about their mom helping them move out or going home on break with their clothes being around the cat allergen.
I had this happen to me but it involved my service dog; she’s a sweet baby and my roommate one of three was “allergic” but she knew months before we moved in that I had a service animal. My dog was registered with the school and state and she still said I wasn’t allowed to have it. She wound up saying I either had to move or the dog had to go; she was then later kicked out of our dorm because she started to harass me, my dog, and my bf only stayed one night because his car broke down.
now if its because she wants her mom to regularly stay over, absolutely not the asshole. let her know that your cat isnt just a pet, it's a tool to aid your mental health. she shouldnt be staying over in the first place. you have paperwork saying you need your cat, if she wants to see her mom she can go visit.
I do get that which is why I’m conflicted. Like I was by no means ever going to let my cat just roam, it would be in my room. And she is not forced to see it either and I love to clean. My thing too is I work with horses too (like almost every day for HOURS) and the moms asthmatic too so I’m confused.