You may not like this solution, but I got allergy shots when I was younger and they really worked. My allergies popped up in college and I have no clue why (stress probably, and they got worse after my wisdom teeth were pulled but that could be either from the surgery or the potent antibiotics they gave me). I did about 4 years of the shots, and they haven’t bothered me since.
Homeopathy could be a good idea, too, if you’d rather go the alternative med route. There might bean easy remedy for dog allergies (not sure), or a remedy that addresses all your issues. That would require working with a good classical homeopath, however.