Some people are allergic to the scales of dried skin, hair, feathers or saliva from animals.
The best thing to do:
Keep pets with fur or hair out of your home.
If you can’t keep the pets outdoors, then:
Keep the pets out of your bedroom, and keep the bedroom door closed. Consider placing a standalone HEPA filtration unit in the bedroom. You may also want to consider HEPA filtration units for your central air-conditioning.
Remove carpets and furniture covered with cloth from your home. If that is not possible, keep the pets out of the rooms where these are located.