Because I have allergies, I never got into pets, at least since I was a kid.
Some of my friends have cat allergies. But, I am a very fastidious clean sorta guy so there is never any cat litter smell or cat hair on my furniture (cause I have to clean it off every day!) You are allergic to the dander. Cats probably trigger it more than dogs do, right? If you have access to horses anywhere, they will not trigger your allergies, and they are very cool mellow animals. Most tame horses are very friendly and will approach humans even if they are in a 1-acre field with plenty of places to run. Also, birds, white rats and most pet rodents like hamsters, gerbils and rabbits will not trigger the allergies.