Yes, heck it's even possible to be allergic to one dog and not another. A friend had two dogs and I would stuff up and my eyes would tear from one of them. If I inadvertently touched my eyes after touching the dog they would itch like crazy. I would also break out in hives in areas where the skin is more sensitive, like the inside of my forearms. I never had that kind of reaction to a dog. We ruled out environmental factors when I realized that the hives on my arm were even worse in areas where she licked me.
Allergy medication took care of the nose and eye issues. If it wasn't too warm a long sleeve shirt prevented the hives. But if it was summer, I would wash off my arms after playing with her and the hives would go away in an hour or so. Of course not playing with her wasn't an option.
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Holly, Misty & their friend, Jake, the dog.
Onyx, Callie May, Maggie & Kobi forever in my heart.
Yes, I know I need a new signature pic...someday...