A purifier for cat allergies in 200sf room

I'm in US, staying in a place where they let a cat in & out. I just found out from allergist that I'm allergic & I never knew that. I've been around plenty & never had a problem, but I'm suspecting it's an issue here.

What's a good recommendation for our room that's about 200 square feet to help with cat allergies? I'm wanting one that's also got a HEPA filter to cover bases of anything that might be a problem. My system is taxed after previous exposure to mold. Hoping not to spend more than $300, but I'll consider whatever will help.

There's a purifier they have running downstairs. I've seen some recommendations that there'd have to be one in every room, but I'm just worried about the one in staying in at the moment.