Well, at this age, we must always consider systemic (internal issues). However, Yes, a food and/or environmental allergy is a very common cause for feet licking. Especially, if its multiple feet.
Here's a ton of info about both types of allergies and treatment alternatives, so you'll be prepared when you talk with your vet.
So, to rule-out food allergies you need to do a diet trial.
Summary: The primary protein in most dog foods is lamb, chicken, or beef. The primary carbohydrate is rice or corn. So, we need to change both. The most popular alternative diets are Venison and Potato, Duck and Potato, or Fish and Potato. It is available in prescription formulas (i.e. Science Diet D/D) or you can find some similar foods at the big pet stores like PetSmart or PetCo. Just make sure that when they say Venison is the "main ingredient" they don't sneak in other stuff like lamb meal or fish meal. Those would be poor choices. A non-prescription option would include Dick Van Patten's brand called Natural Balance. Keep in mind, holistic or all-natural foods are not necessarily any better when trying to remove a food allergy. Chicken is chicken, and rice is rice. When you perform a diet trial, you must stick with the food for 2-3 months to see if there is any benefit. NO OTHER treats or human food can be given during this time period. Another option to really chase after food allergies as the cause of the problem, is to start a prescription food called Science Diet Z/D or Z/D ultra.
Here is some more information about food allergies:
INFORMATION ON SCIENCE DIET D/D, Z/D, and HYPOALLERGENIC TREATS:
SCIENCE DIET FOODS
Also, definitely read about ENVIRONMENTAL ALLERGIES (atopy). Some pets, suffer from both environmental and food allergies:
Atopy (environmental allergies)
If you want to actual diagnose what in the environment may be causing the allergy, you can do an allergy test. Now, you don’t have to shave half the body and do the old grid test on the skin. There is now a rather good blood test that looks for allergies to weeds, trees, grasses!, molds, even house dust mites. You can read more about it here:
Testing for Environmental Allergies
VARL allergy testing
If your veterinarian does not offer VARL, they may offer a comparable company to perform the blood test.
It is important to also recognize, once the skin is inflamed or has an odor, there is likely a secondary yeast or bacterial skin infection present. .
TREATMENT OPTIONS (A small representative list - some suggestions you may have already tried)
1. Steroids. Veterinarians will either give an injection that can last from hours to weeks, or send home oral steroids like prednisone or dexamethasone. Steroids can be safe if not used long-term (several months) and if used as directed by your veterinarian. Frequently, the oral steroids will be weaned down to the lowest dose necessary to keep the allergy suppressed.
2. Antihistamines. A prescription of hydroxyzine is common. Sometimes, over-the-counter Benadryl will help. However, for many allergies, antihistamines alone frequently are not good enough to control allergies.
Benadryl can be given at a dose of 1mg per pound of body weight. Keep in mind, Benadryl tablets and liquids come in different sizes. So, an approximately 25 pound dog can get a full 25mg tablet or a half of a 50mg tablet. I usually avoid the liquid Benadryl in larger dogs (you would have to give too much of it). You can give Benadryl every 8-12 hours.
3. Essential fatty acid supplements. Definitely, if you plan to give an antihistamine long-term,
combine it with an EFA supplement. I prefer the veterinary products, which are already dosed for pets. Your vet
should carry a product on their shelf, or over-the-internet you can look for Aller G3, 3V caps,
EFA-z, or Derm caps. Some vets use a product called Temaril-P. It’s an antihistamine with a low-dose steroid built into the same tablet.
4. Atopica. Neat stuff. Can take a few weeks to be of benefit. Not the most cost-effective, but can
be incredible for allergies when the above does not work. Read the link below for more
5. Your vet should also carry some special sprays and shampoos designed for whatever skin condition your pet may have. One of my favorite product lines is called Douxo. They carry various shampoos designed to calm the skin, treat bacteria infections, and help with seborrhea.
6. Lastly, oral antibiotics and/or anti-yeast medication, if indicated. Generally, your vet will recommend a simple skin cytology test to see what is on the surface of the skin.