I have a cat and have allergy problems partly related to this. I've discussed it with my doctor and there was no permanent 'cure' that he could recommend. But taking Allegra or Claritin for general allergy problems will work for pet Allergies as well. In a severe case you can keep your pet outside, thus limiting your exposure and preventing pet dander and hair from becoming a household problem.
I am severly allergic to all animals including my 2 dogs, my horses, and everything else you can think of. I take Clariton every day which helps ALOT! I also bought Allerpet from my vet. I rub this on my dogs coat once a week and I can pick her up and hold her and I won't start sneezing. It's really great stuff for people who are allergic to their pets. It comes in two different kinds, one for dog allergies and one for cat allergies.
I have severe allergies to most animals with fur basically. I did go through the desensitization for cats and it worked. I used to break out in hives all over my body, the throat would swell up I would have Asthma attacks and have what felt like extreme hay-fever. No tablets helped with this but the round of injections that went for a year or so did help and I no longer have the allergies. I have been allergy free for cats for 12 years now. It doesn't work for everyone though!
We started our yellow lab, Fargo, on desesitization shots about a year ago. I am very frustrated. He used to lick his paws until they were sore and he would limp. Also, his ears were frequently infected. Steroids worked like a miracle but since they're not recommended long term, we decided on desentization. Well, it seems like, instead of being very miserable in the spring and fall, he is now somewhat miserable all year long. I'm not sure whether to continue or not. When they tested him, they found him to be allergic to all kinds of plants, trees, as well as cats, wool, etc. I don't believe these shots work well and they are very expensive and you have to give the dog a shot every 3 weeks. I should have known because I've always heard that people who get tested for allergies are allergic to almost everything...what's the point???