Cat Allergies Treatment

I rescue cats and within the last couple months, anytime I bring a new one home I wake up the next day with itchy/burning eyes, sneezing, etc.
After a couple days it goes away lol I just thought it was odd.

Anyone else experience this?

My roommate has two cats that make my allergies go haywire when they are roaming the apartment. When she puts them in her room, I am fine. However, lately we have only been letting one of the cats out. No allergies! Could I somehow be allergic to only the one cat?
The other cat has long hair and sheds more, while the one we let out doesn’t. He is also a male, while the long-hair cat is female. I have no idea if these things matter, but those are the major differences.

If I got a cat, I would get an air purifier, take allergy pills, and bathe the cat with a special shampoo once a month. Do you think that, by doing this, I will have completely no reaction to the cat?
EDIT: I have mild allergies!!