
Your only real solution is probably to have allergy testing done - expensive unless you have insurance to pay for it. I have a wire haired fox terrier who became itchy at about 18 months old, and scratched and bit herself until she had a scabby back and sore paws. My first vet insisted it was a food allergy (without any allergy testing) and treated by powerful steroids, then tried to insist my dog went onto a special diet. We parted company over the issue of steroid use and special diets.
My second vet (who I am still using) said that food allergies are rarer than allergies to things in the environment (eg. dust mites, pollen). I did find some websites that said the same, but I suspect different vets have different views! Anyway, we allergy tested, found out the cause (pollen, not food) and now manage it quite well. Piriton tablets (the human ones) and Malaseb shampoo are our main treatments. Occasionally, eg. in high pollen season, we have to resort to an occasional steroid injection (I would prefer not to do this, but sometimes it is necessary) and antibiotics to stop the itching cycle. My dog rubbed her itchy back on the carpet constantly, until it was sore and raw. Of course, the raw areas then got infected, which needed antibiotics. It is an awful cycle. I can only suggest that you try allergy testing. It is done in stages and you can stop partway through (we did), if your vet does what mine did, and asks you at each stage.
Poor Max. My Bracken was miserable when at her worst. Fingers crossed that you manage to find some solution.
Claire