Hi & welcome to the forum. Sorry your dealing with allergies. It's not usually easy to figure out. I was wondering whether your dogs vet has looked him over? If he has any secondary problems because of the allergies, they need to be the priority being treated while simultaneously figuring out what is causing the allergies.
It's a good idea to do a food trial if that's what you're planning.. Just remember you have to keep the treats away as well & stick to one protein/carb source for 2-3 months. If you don't do a clean food trial and this ends up being food related, you'll never know what the culprit might be. If it's an inhalant it'll be even harder to pin point. If you don't know how to do a food trial, here is a link with an easy explanation:
dog-with-dog-food-allergy.html
What I would recommend is using apple cider vinegar(organic only!)/water mixture as a topical spray (but secondary problems need to first be prioritized here). And I also like adding apple cider vinegar mixed into the food. Giving your dog a good quality fish oil on a daily basis is a must imo.
I went through a probable allergy with my dog early this year. You can read it here:
Kuma's losing fur to get some ideas of what I've done & some suggestions I was also given on there that might help you. I still think there were more issues with my girl but I may never know what exactly happened since I haven't had real answers. She was also very young which, from my understanding, doesn't happen often w/dogs & allergies.
I hope you can figure out what is causing your Cosby problems. Good luck!