Keep in mind that if he’s allergic to turkey, he’s highly likely to be allergic to all fowl. You need to find a food that doesn’t have ANY chicken, egg or any other feathered relative such as duck. No chicken meal, by-product, fat, dried egg, etc. You need to look at the entire ingredient panel, even dried egg way down at the bottom of the list can be enough to set off an allergic response.
The only dry foods that were completely chicken free last time I looked was Acana Pacifica and Orijen Six Fish. Which may be more than you want to spend. Although keep in mind, they’re much lower in carbs and he’ll be eating less than his current food so it’s not quite as bad as it might seem from the price point.
Some of the kibbles have hydrolyzed processing of proteins like chicken, which supposedly means that it won’t cause an allergic response. I haven’t dared to try it with my allergic kitty, but I just got a free sample of First Mate kibble that features that. I don’t know the price point on that though, or whether it will fit your other nutritional needs.
I ended up feeding raw to my allergic wonder, she gets beef sliders from a local company called Small Batch. I fed 95% canned beef for awhile, but she would periodically still flare up, although not too badly. Probably from the manufacturing process leaving trace allergens when they switch flavors during canning would be my best guess.
Once you switch to a novel protein with ZERO feathered friends in it, you need to give it 6 weeks to see if there is any relief of symptoms. And it has to be strict- no treats or anything apart from the designated food. You can ask your vet for a steroid shot to give him immediate relief, but factor that into the food trial- you’ll want to go a few weeks longer to make sure the new food is working out for him without the influence of the steroid shot.