I agree with your vet that an allergy could cause the skin to become very sensitive and itchy. The most common allergies in dogs are food allergies.
There are actually allergy tests for dogs and they work just like for humans. A patch of skin has to be shaved, then droplets of common allergenes are applied to the skin and the spots are marked. Those spots that turn red show the allergies of the dog. Please ask your vet if such a test is available there.
If your vet doesn't have the materials for a test, you need to do a similar test yourself. There are special allergy foods available for dogs. These contain only proteins from one single animal species - for example only fish, duck or deer.
- Make a list of available foods and the protein sources (animals) in them
- Buy enough of one kind of food to feed your dog at least 3 weeks with it.
- Feed your dog nothing but one type of allergy food for 3 - 4 weeks. No treats, no mixing with other brands or flavors, no leftovers from human food.
- If you don't notice an improvement of his symptoms, change to a food with a different protein source and repeat the process.
This is a lenghty process, but hopefully you'll find a suitable food for your dog. I know several people who went through the same process to find the right food for their dog.
It's very important that the food actually only contains meat from one type of animal. There are some foods advertized as "allergy food" or "sensitive food" that are basically normal food (mix of proteins from several species) but have some additives mixed in that are supposed to make the fur look better. If your dog really has an allergy, those types of food won't be able to alleviate his itchyness.