It is possible that your pup has multiple allergies.
Food allergy is very possible with her as well if she seems to be itchy all year round. Dogs with food allergies tend to lick and scratch their paws, face and ears the most, but any of the "allergy reactive areas" like her axillary areas (armpits) can be affected.
Make sure that the food that you are putting her on is a true hypoallergenic diet. The trouble with "limited ingredient" or "low allergy" pet store brands is that the same machinery is used on multiple lots of food without sterilization cleaning in between. So for example even if a food says it has salmon and rice if the previous batch had beef and corn then you will get traces of those ingredients in your bag of food. Not a big deal if your dog isn't allergic but a waste of money thinking that the food was hypoallergenic and not good for your dog if those happen to be allergens for your dog. The veterinary brand true hypoallergenic foods are more expensive because it isn't cheap to thoroughly remove all traces of a previous food mixture from the machines used to process food, but the only ingredients in that food is what is listed on the bag.
If you based your diet upon blood tests please understand that blood tests for food allergies are much less reliable than those for inhaled allergens, meaning that her tests may be false negative. That means that food allergens may not show up positive even though she is allergic to those food items.
Generally what I recommend is trying to clear the skin with a prescription hypoallergenic food and then adding one food item (chicken, beef, corn wheat etc) every month to see what they react to. Then we can find a regular food to try that does not contain those foods she reacted to. As far as permanent diets I do tend to stick with Purina Pro Plan brands or Nature's Recipe as I find those rarely if ever have cross contamination. Purina Pro Plan Turkey and Barley or Nature's Recipe Vegetarian or Venison are pretty good products. I know that this isn't easy from personal experience (my dog is allergic to wheat) and it is time consuming, but worth it.
If you choose to try testing/treating her for a food allergy I recommend that you try a true hypoallergenic diet like Hills z/d or Purina Veterinary Diets HA. No treats, flavored medication or bones while on the diet. A hypoallergenic diet must be used for a least 12 to 16 weeks to see the full effects. You should see some improvement in 6 to 8 weeks.
Best of luck with your pup, please let me know if you have any further questions.