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Hello and thank you for using this site to help you. scratching around the face is usually an indication of airborne allergies. You may also see the dog licking the feet with such allergies. You may actually be looking at a combo of food and airborne allergies but having changed the food in April may not be enough time for the dog's system to work through it. It can take up to 6 months or more before you see relief from a food allergy and only if you are cutting out the food the dog is allergic to. Most are allergic to grains, chicken, beef, and lamb.
I would talk to your vet about Apoquel for allergies and see if that stops the scratching, If so, you know you are dealing with allergies for sure. Aside from allergy testing which is expensive, there is no way to know the culprit but March would start many airborne allergies so it may be coincidence that the teeth were cleaned and the allergy started.