I have very bad asthma and my allergies are even worse! My border terrier sleeps with me every night!! The only time I experience symptoms is when he plays with other dogs and the dander from the other dogs are on him. Other than that he is great to have!
Border Terriers don't shed much at all so what you have heard is incorrect
my daughter has mild asthma too, but they are fine together, she does shed a little, but what does come out falls straight to the floor and does not float around like the finer haired dogs. but a well groomed dog shouldnt shed much at all.