I really don't see what difference it makes if someone else's dog is allergic to sweet potatoes. What you need to know is what is your dog allergic to.
That's what a visit to a Dermatology Vet for allergy testing might help you determine. Otherwise it's just guessing. Probably not cheap, unfortunately.
Are you even sure it is a food allergy? In my readings it's more common to have environmental allergies than food. My boy's environmental allergies are seasonal, pollens and grasses, so at least he can go off his meds in winter.
Good luck, it's awful to see them in misery.