I am allergic to almost everything and have asthma too. Since my insurance no longer cover Allerex which is Dallergy, I have to take over the counter Zyrtec D or Claritin D. (which you get from your pharmacist)

There are no actual antihistamines that work just for pet allergies (most work for ALL allergens), but many do work like the ones I mentioned. I noticed you didn't say you tried these, these used to be prescription only until a few years ago.

As far as the testing goes, it can be very painful and expensive. (believe me I know and if you don't like feeling of tacks put into your back, than you don't want to do it). THere are other kinds of tests, but this one is the most reliable. But no matter if the test confirm the allergy or not, it is still treated the same way. So I say, save your money and just get some Claritin D. It will take a couple of weeks to get the full effects of the antihistamines. Good luck. I am allergic to dogs too, and there is no way I am getting rid of my pets. Now the carpet, was worth it though.