There are two types of allergies, food allergies and inhalant allergies.
In order to positively identify an exact allergy is through allergy blood tests, the same tests basically that you or I would have done in a similar circumstance. With these results a serum can be derived to help to alleviate the problem.
This, initially is expensive, but the only true way to determine the exact source. If it comes and goes with the changes of season, then it is most likely inhalant and not food. Temporarily you can give benadryl but talk with your vet first for the exact dosage.
Science Diet does make a real good allgery food called z/d. Be willing to use it for 30 to 60 days. If during that time the problem is reduced or goes away, and gets worse when returning to old food, then there is the answer. During the time you feed the z/d, you have to remove 100% of everything else. No treats unless it is raw vegetables like green beans, broccolli etc.
I had a dog with both inhalent and food allergies and it was a pain to deal with day in and day out.
Breeding and Training Boykin Spaniels, a True American Gundog