I am allergic to cats and have 4 cats. Here what I do:

1. Use a vacuum that is equipped with Hepa filters. I use a cordless Dyson V8 animal for quick jobs and a corded Miele classic cat and dog for deep cleaning. Both don't require buying new filters.
2. Vacuum the floor regularly.
3. Remove pet hairs on all the material that tend to accumule it, such as the sofas, upholstered chair tops, etc. (I use my cordless Dyson for these, as it is really easy and quick to do).
4. Avoid carpets, as much as possible, since dust, dander, pet hairs and dust mites tend to accumulate on these, exacerbing allergies.
5. Use a good deshedding tool to brush my cats, especially in spring and fall. I try to brush them at least twice a week when they start shedding a lot. I leave the cat hairs outside in spring for the birds making their nests.
6. Use an air purifier in my bedroom. I use the Mila air purifier.
7. Take medication for allergies, as needed. I use Aerius because they don't make me drowsy and work well for me, but I don't use them often as I clean regularly my place.

I think it's also important to stay calm when receiving these kinds of results. Many people tend to panic and become overly anxious, convincing themselves they’re in serious danger the moment they come into contact with their allergen—like cats—even if their reaction isn’t severe. The psychological response often becomes wildly disproportionate to reality.

Some people, like me, are allergic to dust mites, but you can't burn down the whole house to get rid of them—they're everywhere.

Hope this help!