I am just seeing this. So sorry. He must be miserable. Not sure what you mean by sweating. Dogs don't really sweat except through sweat glands in their paws. They heat exchange by panting. That being said, I am not sure what testing your Vets have done. Have they done any skin scrapings or allergy testing? Have you tried various diets? Have you maybe tried a grain free diet and possibly one that is fish based? Are there any Vet schools/universities within travel distance for you? Yes, you have spent a good amount of money but your dog may need to be seen by a Canine Dermatologist and/or allergist and have testing done.
These issues can be very hard to deal with and nail down. Hope you might be able to hang in there and see if this can be managed.
Please come back to update.