I don't have experience with food allergies but I did want to tell you about my husband's experience with pet allergies in case any of it helps. He has had a number of allergies for a long time, but it was mostly restricted to outdoor allergens like different kinds of pollens. In the last few years he has also developed indoor allergies, and is now allergic to cats (we have 3).

His allergist recommended keeping the bedroom door shut at all times, so at least his sleeping areas are free of hair, and this has helped a lot. Make sure you keep your freshly cleaned clothes in an area your cats can't access as well. We bought a couch that can easily and quickly be wiped down for downstairs where my husband spends a lot of time (he gets areas of raised, red skin that is itchy. Not necessarily hives because they are restricted to small areas, but could be related to contact with allergens). The allergist also recommended bathing the cats weekly, but this didn't really seem to make a lot of sense because after they were bathed, they obsessively licked themselves (and saliva is mainly the allergen). There are wipes that you can buy too that are supposed to removed dander that may or may not help.

Good luck with all of this.