Changing foods from over the counter food to another one otc isn't likely to help. Dogs with allergies either have seasonal (environmental, or atopy) or food. The food allergic dog is typically itchy year round, and needs to undergo a prescription, hypoallergenic food trial for 8 weeks while receiving no treats, people food, flavored heartworm prevention (I use Advantage multi so they are still covered during this time) to see if they respond. Usually dogs are allergic to the protein source (chicken, beef, etc).
Atopic dogs (environmental allergens) are itchy off and on, tends to be worse in spring and summer (although in Houston it can be year round). 75% of these dogs respond to immunotherapy, which takes a while to kick in (upwards of 6-8 months) after performing allergy testing. In the meantime, doing antibiotics, anti-inflammatories, medicated shampoos, wiping the feet daily, etc. will help manage it.
Antihistamines are fine however off-label, benadryl is 1mg/lb twice daily, you can also use zyrtec and claritin, at different dosages. Main side effect is sleepiness.
Apoquel works wonders for most dogs though not all. It will relieve the itch about as well as Prednisone with less side-effects. However is a little pricey.