If you switch to a high quality grain free food, you will see improvement in as little 3 days, may take up to a week.

Try a grain free kibble, if you don't want to go to the Veg to Bowl which Ellie/Pomzu mentioned.

Also, track down this book and give it a read:
The Whole Pet Diet, by Andi Brown.

I found it at my library. She gives so much information on which foods do what, which herbs will help. AND she includes recipes.

I am currently using the Veg to Bowl, and the Spot's Chicken Stew recipe from the book. NO issues! Itching stopped, the gunk build up in Marlin's eyes cleared up. Poor guy has lived with that for his 11 years and by switching foods, it cleared up in less than 5 days.

The veal and rice is nice, but I bet it is costly and who knows, the rice may still be an issue.

Good luck, which ever route you choose. Learning about nutrition and reading labels is just as important for our pets as it is for ourselves.