I agree with Coppperbelle. Supplements like "nzymes" have tons of stuff in them, and when you're trying to figure an allergy out, you want to limit the number of different things the dog eats. Like coppper said, start with a food, no cookies other than kibble, and go from there.
The only thing I would do though, is keep the dog on it for more than a month. As long as the dog isn't getting worse, and there's no doubt that the dog is not getting any worse, I'd stay on it. Some dogs can take months to get rid of the reaction, even if the food they're on doesn't have the allergen.