Hi again...
Okay...don't take this the wrong way, but from they way it seems (perhaps) your vet is handling this, he may not have the necessary understanding of allergies. I suggest a Vet Dermatologist.
Right from the start, your kiddo should have had a skin scraping and a culture - both are simple, quick, and very diagnositic (and, can provide clues to relief!).
The fact that it seems the vet didn't even rule in/out whether this is a skin infection...is...not good. If this is staph intermedius (pyoderma) or fungal - it has to be treated. When skin/ear etc. infections are chronic/recurrent - there is something else going on, as skin is an elimination organ - so it's either 1) allergies or 2) secondary to a disease (hence, bloodwork needed).
If food was seriously suspected (only 10-15% of allergy cases), chicken should've been eliminated by the vet right away. Chicken and beef are known protein-source allergens. So, even if it is/was food allergy...the path taken by the vet didn't likely eliminate the right things for your baby.
A Vet Derm could likely figure this out very quickly. While it could be a food allergy, it really wasn't approached very well by your vet and I feel really bad for you and your kiddo - but try not to worry, I've been there too - and this is my vet derm's FAQ page, scroll down, click on "food allergies", for one, but there is all kinds of good stuff here (photos too):
Dermatology for Animals