I think it is possible although it sounds weird. As to pink eye, it is the bacterial or viral infection or allergic reaction. It cause watery eyes, redness and dryness of eyes, swelling eyelids, blurry vision, strong foreign body sensation and increased sensitivity to light. Some people might be allergic to the pets' dander so that it causes allergic reaction, the similar symptoms to other two kinds of conjunctivitis. If you are sure that your pink eye is caused by the dog dander, you should avoid close contact with pets. As to allergic conjunctivitis, it goes fast if you get away from the allergens. If the symptoms persist, then you should go to hospital to find out the underlying roots.