You are right to suspect allergies (food or environmental) for his excessive licking/gnawing of the paws. I know how frustrating this can be for him and you, I am sorry. I am going to make some recommendation if no improvement I would discuss with your vet about a prescription food called z/d and possibly the use of a medication apoquel. In the meantime, this is what you can try:
1- Change his diet to a grain free diet with a different source of protein than what he normally has had in the past. For example: If he seldom ate fish then put him on a food that has fish. When on this diet he should not eat anything else or he will not improve. Needs to be on this diet for 6-8 weeks before you see significant improvement. No people food, for treats you can give veggies like broccoli, baby carrots, cauliflower, etc.
2- Start him on Benadryl (diphenhydramine) 25mg every 12 hours. You can buy Benadryl (diphenhydramine) over the counter in any pharmacy (shemist).
3- Supplement with Eicosaderm (omega 3 fatty acids); you can buy this over the counter in any pet store or online. Give at label dose.
For the paws this is what you can do:
1- Need to stop him from licking or he is going to delay healing. Pick up an E-collar (cone) in your local pet store to stop him from licking/gnawing the affected area.
2- Pick up in your local pharmacy "Hibiclens" antimicrobial soap or chlorhexiderm scrub. Wash area with this soap 2-3 times a day. If you do not find the above soap use over the counter antibacterial soap.
3- After washing affected area as above apply a topical antibiotic like neosporin or bacitracin. Do this 2-3 times a day for the next 7-10 days. You can buy this over the counter in any pharmacy (chemist)
4- If no significant improvement after doing the above, follow up with your family veterinarian.
My goal is to provide you with excellent service - I hope I've provided the information you were seeking, if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate me when you are done.