Oh boy I can relate to this question.
I grew up with many dogs, a cat, horses, goats and cows. I have terrible pollen allergies. I spent most of my childhood in an allergic haze (it was awful). I never did allergy shots because my mom didn't think they helped her any.
I have one son with 41+ food intolerances (similar to allergies).
I have been so afraid of my son living the way I did that, after a couple of bad attempts, we gave up on having a dog. Finally, after all these years, we adopted a mini schnoodle puppy (poodle/schnauzer combo). She is supposed to be low allergen (non-shedder).
When we first brought her home my son and I both broke out in hives. It was so heartbreaking. I sent her up to my mom in TN for a few weeks while we decided what to do.
We started seeing a chiropractor who specializes in allergies and a technique called "bio-set" (similar to NAET). We tightened up our diets again and cut out certain offending foods. We also do acupuncture. To my great surprise, when our schnoodle came home (on Christmas Eve) we seemed to be OK. I had already prepared my kids that she might have to go live with Grandma. But, here in May, she's still with us. And we don't take ANY allergy meds. For other reasons I will not allow my son or myself to be on any long term antihistamines (other than the occasional benadryl). That was a condition of our keeping the dog.
Through the years, a couple of different integrative practitioners have explained to me that allergies are a bit like a boiling teapot. It can easily handle a certain amount of water - but put in too much water and it boils over. Another analogy would be marbles . . . you can only hold so many at one time.
So my thinking is to cut down the number of allergens, even if they are seemingly unrelated to the dog (for us dairy and wheat are huge offenders, and for me - soy). I also have an amazing air purifier that I love.
So far so good. We are just nuts about our baby and she has been so wonderful for my sons, especially my younger one who had a bit of fear about dogs.
Good luck - I hope you can work this out.