It's very unlikely the allergies have anything to do with food; only about 10-15% of dog allergies are related to food. I'd recommend you just at least choose a grain free food as dogs with allergies tend to me much more vulnerable to issues w/ grains.
These symptoms are likely due to environmental allergies (pollens, dust, mites etc), and allergies are very common among yorkies, as any Vet Dermatologist will tell you.
I'd get your baby on either Apoquel, Cytopoint, or Atopica asap. Some dogs do have only seasonal allergies - but my 3 babies who have had allergies are all year round.
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