Some people develop an immune reaction to a certain protein produced in the sebaceous glands of a dog's skin. This allergen is found in a dog's dander -- the minute scales of dead skin that dogs are constantly shedding. Allergens are also present in a dog's saliva and urine and are deposited on her fur when she licks herself. When the fur dries, the microscopic particles flake off and become airborne, making it easy for them to get into your nose (and lungs).
If you are experiencing allergic symptoms like wheezing, sneezing, or rashes, consult an allergist. There are many types of allergies, and yours may not be pet-related. If you turn out to be allergic to dogs, your allergist can design an appropriate regimen of medications, alternative therapies, or allergy shots to alleviate much of your suffering.