First off, I know someone who was severely allergic to horses, and she had a prescription from the doctor (I'm sure she got tested), I'm not sure all what she was on, but she took her pill prescription 30 before getting to the barn, she would have an hour lesson, so would be there for maybe 2 hours tops, when she got home, she would take off her clothes in the garage, and her parents would wash them for her, she would shower, take another pill, and I'm pretty sure she was taking something else more "permanent" than pills. She told me once though that she was quite literally deathly allergic to horses, so had to be EXTREMELY careful, but for her it was worth the work.
Second, obviously everyone is different. But I worked with a Curly Arabian cross, had the awesome curly coat and everything, with an arab head, and my allergies were no less obnoxious around him than any other horses, and to point out, same with dogs. I am actually worse when I'm around the "hypoallergenic" dog breeds. Poodles make me worse as well as my friends labradoodles. I would honestly invest in going to the doctor, getting tested, and get a prescription medication, and I always wear a mask when working in the hay shed, and while I still get stuffy, it does help a lot with how bad I get.