Are you allergic to certain pet or pet product?

I've developed a host of allergies in the last decade and I'm now allergic to cats, ferrets and apparently skunks! The latter two don't really make much difference to my general life but being allergic to cats can be a little embarrassing. I've realized that if I go to someone's house and they have a cat I begin by feeling lightheaded and sneezy but I also gag like there is a bad smell. I have to explain that I'm not inferring that their houses smell but rather that their cat is making me ill!