I did have a Westie in the past that had severe allergies to….storagemites, which is in every dogfood that has been stored for a few weeks or more, i.e every food known to man, so he was on the raw diet, did great, he was also severly allergic to fleas, or the saliva from the fleas and to mold/mildew, which living in houston Tx there is a lot of. Poor guy was miserable, until we did the raw diet and decided to keep him inside all the time, when the other dogs went out to play he had to stay in..and it is funny he wanted to go out and the other dogs wanted to come in...figures. The few foods out there that are supposedly good for allergies according to my vet is grainfree ones,
Dick Van Pattens sweet potatoe and duck, I believe was one of the ones he recommended. Try to keep the ingredients list as small as possible, cleaner food means less irritants. Just like our food, the less junk we eat the better we feel...
Good Luck, I know how hard it is with a dog that clearly is bothered by something and you don't know how to help it.
I do know that Petco and Petsmart here in Texas will take food back even though the bag has been opened, which is nice if you are having to try various/numerous different brands until you find what works.