Definitely start with the food. I would go grain-free and a novel protein source such as venison, rabbit, bison, etc. Those seem to be more hypo-allergenic proteins. It takes some time, up to several weeks, to see improvement. I also add coconut oil (organic, extra virgin, I use Barlean's brand) to their food and it can also be rubbed onto their skin.
Good luck, hope your baby feels better soon