No the odor emanates from all the pores of the skin. and it will be a reaction to a given food. rather than any other reactions. like itching,body parts. the dog may show no other reactions than the smells.you would be wasting your money on an allergy dermatologist. as it is close to 1000.00 for those tests!
the least expensive/least evasive action is the food source!
But as I have discovered many times. the individual dog does not process the base of meat which is usually a rancid combination of meats/by-products/oils/grease from the rendering plants to make the food. You can open a bag of good food, and smell. and then open a bag of common food from a pet store/petsmart/grocery store. and smell. it will make you sick!!! and defiantly remind you of grease/stale grease!