If you've never experienced the allergy symptoms before being around dogs and suddenly started experiencing the symptoms of allergies when around dogs then you're likely allergic to the dog or dogs.
Some signs that you're allergic to dogs include, sneezing, coughing, wheezing, itching and swelling around the nose and eye membranes or even redness of the skin after you've been licked by a dog.
If you're experiencing allergy symptoms around the dog then try staying away from the dog for a day or so and see if you're not experiencing those symptoms.
And if you're only experiencing the symptoms of allergies when around the dog and not when you're away from then the dog is the culprit of your allergies.