Animal dander is dead skin or scales from animals. Dander, urine, and dried saliva (especially from cats, but also from small animals such as mice and gerbils) are common allergens that can be spread throughout your home by indoor pets. Hair is often not the problem. Short-haired animals are no less of a problem than long-haired ones.
If your allergy symptoms are caused by your pet, you may want to consider finding your pet another home. You will have to decide the importance of your pet compared with the severity of your allergy symptoms. If you do decide to find another home for your pet, clean your home well to remove all allergens after your pet is gone.
There are some less severe alternatives to giving your pet away.
WebMD Medical Reference from Healthwise