Food allergies are extremely rare, so changing foods likely won't do a thing for symptoms since the kiddo prob has enviro/pollen alleriges, as evidenced by paw licking. Read here on how to approach and treat allergies:
http://www.yorkietalk.com/forums/die...tart-here.html
The air licking can be from reflux, dental issues, dry mouth/throat/scratchy, nausea, allergies...