I am sorry to hear Willie is so itchy. This could be allergies, but it could also be things like autoimmune disease, skin parasites, infection. Were any tests such as skin biopsies or skin scrapings done?
Do you use flea control on Willie? Fleas and their saliva are one of the most common allergens in dogs. Even if you are not seeing fleas, you should use a good flea product such as the Seresto collar or Frontline. When a dog has become hypersensitive to fleas, it only takes one or two to set them itching and scratching; and you can't see a single flea on a whole dog.
Food allergies can cause intense itching of the face. Feeding a homemade diet may not help. When dogs have food allergy, they are are allergic to a particular ingredient, which can be any protein: chicken, beef, wheat, rice, etc. Just switching brands of food, or switching to homemade diets may not eliminate that ingredient. When you try treating a dog for food allergy you have to eliminate everything he eats now, and chose a "novel protein" diet, or limited ingredient diet containing ingredients he has never eaten before, such as a venison/sweet potato diet or rabbit/potato. You feed nothing but this diet of 6 to 8 weeks, no treats or table food. If the itching improves, then it is food allergy.
Another option is a "hydrolized protein" diet such as Hills Z/D or Royal Canin HP. Again, you feed only the diet, nothing else at all, for 6 to 8 weeks. You can get these from a veterinarian or from Chewy.com but they contact your vet for permission to ship it to you.
If it is environmental allergies, changing the diet to homemade or grain free won't make a difference. Unless you can identify the allergen, you have to treat the symptoms with steroids, antihistamines, and supplements. There is a new allergy medication, called Apoquel that really helps about 80% of dogs with allergies, sometimes in just a few days. It is a prescription from your veterinarian.
Please let me know if this helps, and what other questions you have. It is so frustrating when dogs have allergies, because there is no cure yet.