There are several treatments to lessen eyelid bags as a result of chronic allergies including topical medications,various surgical procedures or laser treatments around the eyes. You're on the right path to try to treat the source and keep the allergies under control as any of these procedures mentioned will not cure allergies. Working with an allergist and eyelid specialist can hopefully Improve your condition.
You may be a good candidate for hyaluronic acid fillers (ie restylane) to the lower lid/cheek junction. Once you get your allergy symptoms stabilized, seek an evaluation by an experienced injector around the eyelid area to see if you would benefit from injectable fillers.
I have looked at your pictures and believe the swelling to be secondary to your allergies. When the swelling occurs in your nose and face this causes venous congestion in the area. Because the lower eyelid skin is the thinnest in the body any back up of blood will cause discoloration here. Treatment of the allergies with an antihistamine or even a nasal steroid should help. Should the discoloration persist, occasionally a hyaluronic acid filler such as Resylane or Juvederm can help if placed in the correct fashion. Good luck to you.
Based on your photos, I would not recommend any surgical options for you at this time but I think an injectable filler would work well for you. I would recommend using one of the hyaluronic acid fillers for the under eye area.
Allergic shiners is just something that a pediatrician made up to confuse mom's. First a moisturizer on this skin is actually helpful. It does not cure the circle but it does make the skin look better. Restylane filler is the best option here.