Hot Rod was so itchy when we got him. Our vet recommended medicated shampoo and medicated conditioner. I don't know if the food change or the sham/cond did the trick but he has been good for 18 months now.
Food changes take some time to work through so keep that in mind if you think there may not be any relief from a different diet. Good luck.
As a quick fix, you can try one of my collars for your little one. I have a customer who uses one on each of her two for itching.