Food allergy is less likely but can't be ruled out with the given information.
Food allergy is not localised to a pinpoint area. It's more generalized. Pruritus related secondary erythema and then scab formation on injured areas may form these kinds of lesions.
Next Steps
Food allergy diagnosis requires meticulous attention. You have to rule out bacterial fungal other probable hypersensitivity causing agents.
Health Tips
Consult with your vet. Novel diet works in diet related hypersensitivity reactions, if other issues are properly taken care of. Hope this helps. thanks