could this be food allergies?

My chihuahua puppy has had really itchy legs and chest area lately.He does not have fleas, and I haven't had him outside (I'm waiting for him to finish up on vaccinations before i take him outside) He is on Hill's Science Diet puppy food, which is what i've been feeding him since I got him 2 months ago.

Legs and chest area suggest perhaps an allergy to a carpet or blanket he lays on. My mom's golden retriever is allergic to several types of wool, among other things. Get him tested at the vet to be sure.

More likely an allergy to something in your home than the food, I think. Are you cleaning his bedding in detergent or have you bathed him? Also, check to see if you are petting him after moisturizing your hands or even after washing. Delicate puppy skin can certainly be irritated by even residual chemicals in these items.
Hope he gets better fast!