Because of the immune system's maturity, it'd be very VERY rare for allergies to happen in puppies. However, it can happen, for whatever bizarre reasons. It would be more likely in a yorkie who is at least 6mths or older, as compared to a younger one.
Food allergies are very rare, they only occur in about 10-15% of allergy cases. Enviro allergies are more common...ie dust, pollen, trees, grass etcetera.
Benadryl rarely works in dog allergies, but I wouldn't worry about the tiredness if you wnat to try it as that will wear off. The issue w/ giving Ben is that you have to give it 4x a day as its half-life is so short. Rather, Vet Derms recommend using either Zyrtec or Claritin for dogs, as they only have to be given once every 24hrs....much more practical!
For more thorough info on allergies, read this thread:
http://www.yorkietalk.com/forums/die...tart-here.html
Where is the itching, btw? And what are you feeding?