It wasn't a food allergy situation, but growing up my family adopted two kittens (a brother and sister) from a local farmer. We were told they were about three months old, but it soon became clear that they could not stomach regular cat food (so we suspected after the fact that they were younger, too young to have been taken away from their mother). Even plain milk would cause them to have the runs, and they weren't always making it to the litter box.
So my mom made them chicken and rice for a few months and eased them back onto a regular cat food diet. I would joke that she spent more time cooking for the cats than she did for us kids.
I don't know if you can take anything away from this other than that my family also cooked for our pets, though. Turkey and yams sounds like your dog is going to be living large.
You also might try searching on line for hypoallergenic or all natural lines of dog food. They are way more expensive but might be necessary for your dog. Your vet should have some sort of list of stuff like that.