my dog mac has the same issue with his paws. he will sit there and lick them until the entire top of the pad hangs off and i have to clip it. i have taken him to the vet and they couldn't figure it out either. mac is about to be four and he has always had a corn allergy but nothing like this. i know a old dog woman who had me try something different. I give mac a injection once every month or so. the medication is called IVERMAX. administer about 1cc of the medication under the neck skin just like you would do for a normal routine vaccination shot. you can get this medication at any local farm and feed store like a co-op supply. this medication is usually for cattle and swine so dont mention it being for your dog. it seems to work for my boy mac. i am able to trust that he wont chew or lick when he has this shot. mac is 50lbs so i give him 1cc a month. adjust dose for certain weight of your animal.
i also firmly suggest the raw diet. when i can afford it i feed the natures variety chicken raw diet. 100% absorb able and a great diet for any dog. mac thinks its like candy for him