Several options. Avoidance of the animal is the most effective treatment. If it too difficult to avoid animals, try reducing dander in home...get animal out of bedroom, purchase HEPA filter, wash animal twice a week. Try medicines like oral antihistamines and steroid nasal spray (both over the counter). See an allergist, allergy shots to animals are a possibility.
Partial help. I assume that you develop allergy symptoms around pets. Any anti-histamine will provide some help. Preferably you should avoide pets. If not, take an otc antihistamine such as fexofenadine or Cetirizine before encountering a pet. If that is ineffective or you own a pet to which you are allergic, you may need to see an allergist and be desensitized to the pet (allergy shots).