My (27f) boyfriend's (31m) health issues are keeping us apart

My boyfriend and I have been together almost a year now. He has severe allergies to the point where he gets sinus infections about once every couple of months.

Recently, he got a pretty bad sinus infection that seems to be lingering. When he gets sick, he doesn't like for me to be over at his place because I currently live with 2 cats and feels like I worsen his symptoms when he's around me. Keep in mind cats are one of the things he's allergic the most to. I try to do the best I can to be allergy free around him. I only go to his house, he doesn't come to mine. I take a shower when I'm over, I have designated clothes that I wear over there that haven't been at my house, I keep clean clothes and a lint roller in the car, I don't go to my house if I want to spend the day with him just so I don't get contaminated,etc but recently he feels like that isn't enough. So I didn't get to see him for a month, which was hard, but I understand he just wants to feel better and I want him to too. So I kept my distance and then I finally got to see him and it was magical! I had missed him so much! But then his symptoms started again and now he doesn't want me to come over again. Mainly he said his neck hurts and feels stiff, which I think is more of a muscular issue than a sinus one, but I guess his lymph nodes could be swelling up.

It's been really hard on me lately and I'm trying not to take it personally because he still chooses to be with me despite the allergies, and I definitely care about him and would rather be long distance than to make things worse, but that thought that maybe he's better off without me always lingers. It's just kinda taking a toll on me because I love him but I feel like I'm a burden on him and to his health. And then I can't get to see him, so it makes me feel very lonely and sad. He hasn't even stepped a foot in my house for 6 months, which I was fine with but now I've realized he hasnt been in my world in a while. He hasn't seen me in a place where I'm comfortable and can be completely myself and I don't know if he ever could see that and that makes me pretty sad if I think about it too much.

Of course I'm not the only cause of the allergies. He lives with a dog so there's those pet allergies and he may be allergic to his snake. But I wanted to do my part to help with the allergies since cats is the most severe one. I've considered getting rid of my cats but it's a scary thought because our relationship hasn't been the best. I see him as a potential forever partner, while him, i dont really know how he feels. I'm usually the one initiating and invested in our relationship, while him, doesn't really put a lot of effort into it, especially when we're apart. But I don't know if it's just because he doesn't feel good or that's just how he is. So, I don't want to get rid of them for him and then we end up breaking it off or something because they are my babies and me and the cats have been through so much together. And I feel like even if I did get rid of them, it would take forever to get rid of the hair and other allergies completely out of my house.

I'm sorry for the long ramble.

Anyways, is there any advice or recommendations you guys have that I could try to help with this? He currently is taking allergy shots and of course different antihistamines and nasal sprays as well as sinus rinses daily to help with his symptoms. I asked him if we could make an appointment with his allergist or another doctor to see if there's anything else we could do but he didn't really seem up for the idea and has been pretty down and hopeless about his situation lately.