I think avoidance is probably the best natural/non-synthetic treatment for allergic rhinitis as there really is no cure for it. Here are some of the treatments you can try:
1) If you're allergic to pets, you'll have to get rid of them. Sorry!
2) Keep windows closed and run the air conditioner during the summer.
3) Avoid working outside if possible, especially if it's windy.
4) Use a vacuum with a true HEPA filter that will trap most dust mites, allergens, and pollens.
5) Wear a dust mask to sweep the floor, dust the furniture, and vacuum or shampoo the carpet.
6) Avoid certain foods that can cause flare-ups.
7) Wear clothing and sleep between sheets made of natural fibers (wool, cotton, linen) instead of synthetic material.
8) Set up an allergy-free environment inside the house by removing items that offend.
9) Get an air purifier in your house and/or change the filters on your furnace more often.
10) Build up your body's immune system so it isn't so sensitive to allergens.
11) Wear non-latex rubber gloves to wash the dishes, clean the stove, scrub the toilet, or whenever your hands will come in contact with harsh chemicals or abrasives.
12) Avoid perfumed or scented air fresheners.
13) For your personal hygiene, use only products that are natural and free of dyes, perfumes, or other sensitizing ingredients.
Any or all of these methods can help you reduce, if not entirely eliminate most breakouts of allergic rhinitis. You must remember, however, that it can come back if you don't follow some sort of disciplined regimen the rest of your life!