My vet is where I have the allergy testing done. They took a blood sample and sent it into some lab. Cost was about $300. The panels they run test for many things like grasses, trees, weeds ,dust mites, etc. and also food allergies. I'm not sure how accurate the test is and my vet even said it is not totally accurate. You can also have skin allergy tests done like they do in humans where they inject various allergens under the skin and see which ones the dog reacts to. I'm sure that is much more accurate.
Is your dog on any meds to control the itching, biting and head shaking? My dog has been receiving Cytopoint injections about every 2 months and it has totally controlled her itching. There is also an oral med called Apoquel that you give daily. Apoquel and Cytopoint are made by the same company. I like the Cytopoint because it's just once every 2 months rather than a daily pill.
If your dog truly have allergies it is a bugger to deal with. It's been over a year and I still don't know what my dog is truly allergic to and may never know. You may seek out a pet dermatologist or go to a vet school that treats pets. Not sure where you are located but I've had dogs to the vet school at the University of Minnesota a couple of times. They have a lot more resources than your local vet.