It's funny you posted this because I'm having almost the same problem, except mine aren't as bad as yours.
I've always had seasonal allergies, but they weren't bad enough for me to bother with medications, etc. I would use Benadryl sometimes which would help alot. It seems that as I get older, my allergies get worse. It also seems that they have been particularly bad since I got Jackson. I normally don't have too many probs in the winter months, but I did this year.
I have heard of people being allergic to yorkies, although they are supposed to be hypoallergenic. I don't know for sure that my allergies are worsened by my boys, but like you, I could never rehome them!
I will be anxious to see others' replies because I'd like to know too.