How do I make my house allergy proof?
You are going to have to wet clean.  You can steam walls, hire professional carpet cleaning (the ones you rent don't get that hot), spray down hardwood floors with some green cleaner, same for the bathrooms.  

Clean fans super good.

Replace air filters.

Have your ducts cleaned.  Use a company that hooks up a negative air machine - not one that "washes" your ducts.  You probably have a ton of cat hair in there.  Do your returns too.

Wash everything that you can.  Blankets, rugs, bedding... anything that can go in a washer.

Steam clean - or better yet see if your carpet cleaners can clean all couches, chairs, upholstery...