Diesel, the westie in my avatar was almost bald at 6 months old due to his allergies.
It took 3 months and £1000s for the dog to see specialists etc to find he was allergic to Chicken, beef, & 4 varieties of grass for starters.
He ended up on a dry Hills prescription food - could have duck or salmon, all other flavours had chicken included in the hidden in the ingredients.
Your vet must be able to do further blood tests to establish what it is. If not try a different vet.
The dry food & numerous steroid injections he had over the years didn't do his kidneys any good in the end, but he held on for 10 years & was fit enough to catch rabbits for all bar the last month or so.
Our vet recons that wastes are the one dog that its essential to insure as they are well known for allergies & other hard to diagnose problems.(ours wasn't)