Dogs, especially yorkies, are very prone these days to enviro allergies (dust, pollens, grasses, trees, whatever...). The cardinal sign is paw licking and chewing.
I would bet it's allergies - and not to food.
More about allergies here:
http://www.yorkietalk.com/forums/die...tart-here.html
I have years of experience with allergies in 2 of my dogs - and the meds that work best are Apoquel and Atopica.