I had a dog with various protein, grain and seasonal allergies. Amongst all these we discovered he was allergic to "grass", needless to say that was a PITA. The vet started him on plain old Benadryl every day.....lo and behold his contact allergies cleared right up. He took 25 mg of generic diphenhydramine for the last 8 years of his life. I bought it at Costco and got a 360 tablets container for $4.
If the dog has environmental allergies then changing foods probably isn't going to help that much. It'd be like me going "gluten free" to try to clear up my hay fever. Having said that, allergies tend to travel in clusters so where there's one there's probably more. Have your daughter talk to her vet about exploring antihistamine options. If the Benadryl doesn't work there are many other OTC options.
Changing food shouldn't hurt. Usually the first recommendation is to go with a fish based kibble. It's easier to find a fish based kibble without any non fish based ingredients than probably any other protein (plus fish based is usually the most inexpensive novel protein option) so you can really knock out all the usual suspects. The thing about TOTW is that almost all of them have chicken fat in there. The base formula is very similar across the board. It's been a long time since I did food trials, but maybe their Pacific Stream formula is worth a shot.