4 month old is itching throughout the day, any answers?

Hi! I was wondering if anyone had some answers for me. My shiba has been itching and biting his coat (not till he bleeds) a lot recently. He is on grain free food and doesn't have fleas (he use to). His skin is pink, but I think it's normally pink. No hives that I can see. We are also giving him some benadryl but it doesn't seem to be working. My girlfriend is worried he might have allergies or something, while I think it is just him shedding his puppy coat. Any thoughts on what it could be? Thanks!!