Help! Boyfriend may be allergic to catsn

Everytime my boyfriend comes over to my house he wakes up the next morning with a headache, and stuffed up nose, sometimes nausea.

He only goes to my room where my cat is so we're starting to wonder if he's allergic

He owned a cat a couple years ago for a few months but of course allergies can develop.

I'm worried because we plan on getting an apartment together and I'm taking the cat with me. My cat is getting up there in age and I'm a cat person so I was planning on having cats all my life, but I also want to spend my life with my boyfriend (we've talked about marriage)

I dont know what to do. I dont want to choose and he thinks getting tested is pointless because he hates doctors and that wont fix his allergy

Update: thank you to everyone who commented with advice, before the next time he comes over I'm going to wash my sheets, and vacuum the floors really good. I'm looking into humidifiers for when he comes over. I dont want him sick but we discussed a trial run of vacuuming and washing the sheets before he starts taking benadryl because he rather not take a pill if it's not necessary