I think it would be a very good idea to try to change food. Really what will it hurt? Try something grain and chicken free. I like to feed Natural Balance. They have several varieties that are limited ingredient. It will take some time to see an improvement with a change of food. If you purchase from Petco they do have a return policy. Right now I am feeding Sweet Potato and Bison. But they also have Venison, Lamb and Fish varieties as well.
Pebbles was a big time scratch/itchier and the food change worked for her. I also add a tsp of Coconut Oil to their food which also seems to have further helped. Good luck and I hope that you are able to figure out what the issue is for your little one.