I have a 9 year old Staffy that is the same way. Hes allergic to everything. We have curbed his chewing and licking of his feet by doing these things: 1) Allergies are stronger at different times of the year so we bath him 1 a week in a hypoallergenic natural shampoo that has hydrocortisone in it. Bath him in cool water. let the soap sit on the skin for 10 min then rinse thoroughly. Then we rinse his paws in a diluted solution of apple cider vinegar and water. Paws get yeast infections (dark between the toes and pads). This neutralizes the yeast.
2) yes diet. Dogs can be allergic to beef, lamb etc due to those animals eating grass…a grain free ( no rice, wheat, corn, barley, alfalfa, etc) definitely helps. We make our own food, mostly cause ALL dog food is junk. We cook chicken, duck, sweet potatoes, peas, carrots and sometimes make a stew for him or just chop it up into his bowl. We also have a friend who sells dehydrated treats for dogs, beef heart, tounge, chicken and duck feet etc. No store bought treats3) We try to keep the grass cut short and we have dog shoes we put on him from time to time when hes outside, but he hates it. We also put baby socks on him when hes in the house, because rough surfaces, or carpet irritate tender feet which creates a vicious circle. This adds padding and a barrier to stop licking/ chewing. You can put camomile lotion on the paws to ease irritation before the socks go on. We use elastic sports tape to help keep them on. Not tight but snug. It flex’s so it moves with the walking motion.
It seems like a lot of work and it is. Also your dog is only 2. Your dog can naturally build an immune to a lot of allergies. Just remember, ALL dogs are allergic to grains, pollen etc, some just more so than others, especially the bullie breeds.
Hope this info helps somewhat and good luck. Mark