Classic sign of allergies
Paws start to itch. Puppy chews paw, until raw. Bacteria join in, with more itching and burning. Puppy chews paw more. etc etc
You should try for a 3 prong approach to this.
1. Consult with your local Vet as to the appropriate Benedryl (gel caps) dosage per the puppy. The usual range is 1-2 mg per pound. Or alternately get a script from the Vet for Hydroxyzine a longer lasting antihistamine.
2. You will probably need an antibiotic from your Vet to treat the skin infection inside-out. Cephalexins are commonly prescribed.
3. Some Vet's may prescribe an antibiotic-antiinflammatory salve such as Panalog. Likewise a standard OTC triple antibiotic salve with a procaine derivative to take out the sting is also effective. Note something like Panalog is very oily designed to soak in fast before Junior can lick it off. If you go with an antibiotic gel then you will need a lick deterent. Some people use bitter apple although it can sting if the skin is too raw or damaged. I prefer a couple of drops of tea tree oil mixed in with a little bit of the antibiotic salve and gently rubbed on the surface. The taste is very astringent and they will not lick it after the first time.
You might consider throwing in a fish oil supplement (e.g. 1- 1000 mg gel cap per day for a small-medium dog) along with Vitamin-E (dry or succinate salt form).
With the allergy suppressed, and the rest of the above helping the skin heal puppy should be more content not to chew his paw.