As Susan said, the only way for you to properly determine if this is a food allergy is by process of an elimination trial. This is the gold standard.
If the dog is food allergic, one of the worst things you can do is rotate their foods. Find one food that does not cause a break out of symptoms and stick to that. My food allergic dog has always done awful when his food is switched too much due to the fact that I could not figure out what was causing the symptoms. We now have him on one food that he does well on and we don’t change it. It has made him and us happier.
