Can someone who is allergic to cats...live with a cat?

This is probably a stupid question. But I’m REALLY desperate for cheap housing and I found a really affordable place in my city in the PERFECT location with some roommates that, for once, look really cool. Problem is, they have 2 cats. I’m pretty allergic to cats, as in they make me sneeze a lot and even a little bit of breathing trouble.

Should this prevent me from taking the apartment? Is it possible to just…work through it and become immune? The housing search is getting really frustrating. Please advise.