Quoted by BeagleMum
Usually when your dog reacts to multiple kibbles, people will say to go RAW (not that it is a bad thing, just some owners don't feel comfortable feeding RAW).
Most people (me included) will recommend Raw because you can stick to one type of meat with no fillers or extra ingrdients. Kibble has many different fillers, meats, grains, rice, corn, veggies that many pets are allergic to. So it is really hard to eliminate the source your pet is allergic to.
If your dog is having these types of allergic reactions you will have to try one meat at a time as recommended above. Eliminate one by one. No vegetables No nothing except for meat/bone/organs from the same meat source.