I have loads of allergies from dust , all 3 types of pollen to food stuffs and even an anti histamine! i take cetirizine every morning every day of the year, it keeps most of the airborne ones pretty much at a level that i can manage to function with. it is pretty cheap on the net, but like most allergy stuff takes a while to build up resistence.
the cost of one tablet a day is way less than the cost of all the boxes of tissues and the missed days caused by the allergies and if you get to keep your dog all the better. in the mean time, give your dog a bath and/or a good wet brushing as often as you can, often it is the dust or lose hairs that are the allergen rather than the dog, so lessen those and you lessen the reaction. you can always wear a dust mask to help you the first few times.