I think I might be allergic to my cat.

To be clear - she's not going ANYWHERE. IF I'm allergic, it's not severe at all. and I would get allergy shots for the rest of my life before giving her away.
But...is it possible to just suddenly be allergic? I had 2 cats my whole life from when I was 3-14. When I was 14 we lost our house and had to rehome them. I'm now almost 17. This past August (since we have gotten back on our feet), a friend of ours was looking for a home for a stray cat she found, and that's how Olivia came into our lives. I noticed recently that I have seemed to have a mild cold ever since I got her (sometimes it's worse than other times. Like now, which is what prompted me to post this). I was DEFINITELY not allergic to our other cats - and one of them had long hair!
Livvy is clean, she's brushed daily and she's had a couple baths since I got her. Is there even a way to tell if I'm definitely allergic or is it just something that's assumed?
To reiterate - she will NOT be rehomed either way. We're together for the long haul.

This is just something I'm curious about.