Hello.

This is unlikely to be due to him being weaned too early. All of the antibodies are obtained in the first few days of life. After that point, puppies do not absorb antibodies over the gut wall and nursing is entirely for nutritional purposes.

The allergies are likely genetic though as we see it in many line of dogs.

Your best option is to see a dermatologist. They will see exactly what the dog is allergic to and use immuno-therapy to give allergy serum injections and de-sensitize the immune system.

The only other real option is suppressing that over active immune system with steroids (Prednisone) + Benadryl as needed for the itching. Benadryl can be given at 1-2 mg per lb every 6-8 hours as needed.

Allergies are a pain, there is no true cure and each dog is different in what exactly they are allergic to and how they respond to therapy. It is very frustrating for both the vet and the owner- not to mention the dog.

I hope this helps, let me know if you have any other questions.