What you describe could be allergies but it might also be something such as mange mites which you can read about here
Or a skin infection with ringworm
or a bacterial skin infection
Paw licking, itching and skin chewing are often signs of allergies. You may see red staining to the fur in the licked areas or raw spots where the dog chews itself.
The skin itches from allergies, the dog licks and chews trying to soothe the itch, making the skin raw and allowing other infections to set in which may itch even more. Infections such as yeast infections can make the skin smell bad.
You can read about allergies and dermatitis in dogs here
Dogs can develop allergies to foods, even ones they eat all the time, and to inhaled items, and contact allergens such as rug cleaners, cedar beds, or chemicals including lawn chemicals or even flea bites.
You might want to try a different dog food that has no ingredients the same as what you feed now. Diets of Fish and Potato, venison, or rabbit etc. where the protein source is new and there are no grains in the food can work for many dogs for example. Another option is the hypoallergenic diet from your vet Hills ZD. Changing food does no good if you feed the same ingredients. Remember food changes have to include all treats and can take 8-12 weeks or more before you see results in skin and coat.
If this is an inhalant allergy you may find using a HEPA air filter in the room the dog uses most and wiping the dog down with a damp towel when it comes in helps reduce allergen exposure.
You might want to see if some plain Benadryl helps with the itching. A common low dose is 1mg per pound of dog every 12 hours. Do check with your vet about using a med but this one or another may help him a lot. If you choose to use that please read here about cautions
You may want to consult with your vet and consider doing allergy testing.
You can try a Chlorhexiderm shampoo from the pet supply store in case the problem is a bacterial skin infection. Malaseb is another good one to eliminate yeast from the skin. Follow directions on the bottles if you try one.
This breed is also known to have low thyroid level issues and that can trigger skin allergies and infections. The vet can check for that with a blood test.
If your dog is not on a flea prevention that might also help. Just one flea bite can make an allergic dog itch all over. If that is the problem then Frontline could resolve a lot of the reactions for you.
Some people find their dogs do better when they are given omega 3&6 fatty acid supplements such as Derm Caps or Linatone from the pet supply store.
If your regular vet is not able to help you then you may want to see a veterinary dermatologist and this page may help you locate one if your vet can't refer you to one
Hope this helps you!
Sometimes you need to use a different antihistamine or a prescription product such as prednisone or Atopica.
You really should work with your vet on this as the tail area for chewing is a common spot for allergies to show up.
With a flea allergic dog one bite can make the dog itch all over and again the base of the tail area is the common location for flea allergies to show up.
Sometimes dogs will chew those areas if they are having hip pain but you didn't mention any problems in walking which typically you would also see.
This is not likely to be cured by using any topical products but for short term relief if the area looks raw try cleaning it with Betadine iodine solution and then using Neosporin or Triple antibiotic ointment on any sore spots.
Or if its not raw, just itchy, you can try a Lidocaine spray or ointment. This is just short term relief until you can figure out what is wrong.
So many possible things could be the underlying issue that you will really need to work with your vet or a veterinary dermatologist on figuring out just what is wrong.