Yes, you are absolutely correct that chicken is one of the Top Four of the food allergens for dogs. Food allergies develop on repeated exposure. The most-eaten foods are the foods most likely to trigger allergies. Add to that the fact that some dogs are sensitive to the "flavor enhancers" injected into many brands of chicken. (True food allergies, though, as opposed to sensitivity or intolerance, are to proteins, even in foods not thought of as "protein foods." That is, for example, a true grain allergy is really an allergy to the grain's protein.)
Usually, the dog with a true food allergy has been eating the diet containing the culprit ingredient for at least 24 months. (Not always, but typically.)
A food allergy can develop in a dog as young as 5 or 6 months, but this is much more rare than a food allergy in an adult dog.
I got him at 9 weeks and he is now 4 months. ... He has been an itchy puppy since we got him ...
But even though chicken is indeed one of the Top Four (and so is beef), food allergies in dogs still account for only 5 to 10% of dog allergies, depending on the source. That is, food allergies are FAR behind flea saliva hypersensitivity and atopy. (OTOH, a dog with food allergies often has non-food allergies as well. This is why the testing and elimination of culprits is carefully done and carefully recorded.)
Yeast overgrowth is a "side effect" of the allergy. (It can be a "side effect" of illnesses and bacterial infections, too.)
To identify the food allergen, the dog is put on a strict elimination diet. This means that a couple of foods the dog has
never eaten are the only ingredients in the diet. No treats, meat-flavored pills, leftovers, Kong filling, etc.
The proof of the food culprit is when the elimination diet removes the allergy symptoms.
Then the system is challenged, slowly and carefully and methodically, ingredient by ingredient, until the culprit is exposed. That culprit is then removed from the dog's diet.
Unfortunately, there is significant overlap in the body geography of atopy versus food allergies. Both involve the ears, both usually involve the feet. Still, there are hints about which it might be from body geography. Another hint about it being food would be a lack of response to steroids, and another would be lack of seasonality.
You (Cathi) are kinda fortunate, really, if your dog had to have an allergy, to have it be food. Food allergies are definitely the simplest to identify (not easy, but simple, if the elimination diet is done properly). Food allergies are also the easiest to "fix," by withdrawing the offending food from the diet (and holding procurable protein sources in reserve, never feeding them, in case of another elimination diet for another food allergy down the road).
There are many links here and descriptions of the food-allergy mechanism. I'll dig up a couple of overviews.