Food allergies are kinda rare (about 10-15% of all allergies). Have you already ruled out enviro (dust, dander, anything) or seasonal?
One thing to consider is to ask your vet about giving a steroid shot, and then assess what kind of relief, if any, happens afterward. If there is a lot of relief for a time, that can be a clue that it's more enviro/season related than food related. It is is enviro, then your options are OTC antihistamines, Atopica, Temaril-P, steroids, or allergy testing (if you want to do allergy shots).
Poor kiddo! Marcel is terribly allergic to Palo Verde trees (we had him allergy tested) and paw-chewing used to be a big need of his. He is on Atopica, but hopefully over the next year we'll be able to discontinue this as the allergy shots ramp up their effectiveness. I know how frustrating the paw licking is - it looks so miserable
!