What you describe could be allergies.
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.
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.
If this was a year round issue 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 thisshows up at paticular times of year it is possible 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
Any of the anti allergy meds may cause the dog to be drowsy so working with your vet on ones that might work without him getting too sleepy is a good idea.
A prescription medication such as Temaril-P may be something you can use with him during allergy season and you can talk with your vet about it.
You may want to consult with your vet and consider doing allergy testing to see just what bothers him.
If there are any raw red areas to his skin 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. The vet can check for that with a blood test.
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.
You can see if your local pet supply store carries Zymox with cortisone or find it online. I've had good luck clearing up infections with that. You can read about it here
This site goes over ear infections and has another ear cleaner mentioned that had good results
here is just the product info
Ear infections are a common symptom of allergies in dogs.
This breed however can have a neck problem that makes them scratch at the head and neck area. You can read about this here
If your regular vet is not able to help you, and you belive the problem is allergies, 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!