How to relieve allergys without taking medication or using nasal washes?

Avoidance. First, get allergy testing done to know which allergens affect you most. Next, eliminate those allergens from your environment. Dust-proofing the home/office is not entirely achievable, but still helps with dust mite allergy. A pet allergy may cost you your pet! If you are allergic to mold, it must be eliminated from the home or office. The only other option is immunotherapy, or allergy shots.
Allergy shots. They avoid a daily medicine. Also some doctors prescribe sublingual drops that desensitize you to allergens without medicine.