You can try a combination of all the suggestions, 1 st you should get allergy tests, as it may be something else. Take an allergy tablet, and allergy shots. It sounds like your doing everything else, like washing your hands, vacuuming , keeping him out of your bedroom, and such. Some others had a good suggestion of changing your clothes after contact with the dog, throw them in the wash right after, and washing your hands and arms after playing with him. It sounds like your doing everything you can to minimize reactions. I am not allergic to dogs, but I am allergic to cats, I sneeze whenever my sons cat comes in contact with me, or if I pet her and then touch my eyes. It was way worse when we first got her, within the first 2 or 3 days , I started sneezing, and itchy watery eyes. I just made sure she doesn't come into my bedroom, and after I pet her, I wash my hands, as well as I vacuum everyday to minimize hair. We also sweep then sniffer the floors every Wednesday, and sweep, sniffer , and damp mop every Sunday, this minimizes the hairs and dust. It is true that the more you are exposed to an allergen, the more you build up a resistance. We have had our cat for a year and 4 months, and she doesn't bother me near as much as before, I hardly sneeze anymore, and as long as I don't touch my face after petting her, and wash my hands after, I'm okay. You mentioned you have only had your baby for 5 months, so maybe over time, your allergies to him will get better or more manageable to a level, you can tolerate. Another thing you could try, is to bath your baby once a week, and brush him after his bath to minimize hair, and remove any excess or loose hairs. I hope you can find a solution that will work for you to be able to live with your baby. Good luck, crossing my fingers and praying for you guys that everything works out. It must be heartbreaking for you guys. Keep us posted.
Just a little information I also wanted to share with you, a few years back, I remember reading an article about children with peanut allergies. They did a study where children were slowly exposed to peanuts, to build up their antibodies to them. This was done in a controlled situation, and done slowly over time to desensitize them to peanut allergies, so it is possible to build up a tolerance over time.