Some of the common causes of itchy skin and rashes like those you’re describing in your poor Tommy are flea allergy, contact allergy, food allergy and atopy.
The problem is that without a methodical, diligent trial to rule out each possibility one by one, you will probably never work out the cause! I would suggest talking to your vet and explaining that you’d like to get to the bottom of the problem and conduct some trials (if they haven’t already been done) to work through the possible causes. You could also ask about omega fatty acid supplements to improve the quality of Tommy’s coat and specialised shampoo’s and conditions. Anti-inflammatories are fantastic at treating the itch but long term use is usually avoided.
Fortunately in recent years new drugs have become available to treat skin disease. These may or may not be suitable for Tommy but certainly worth investigating through your veterinarian.