Hey Vivian,
It sounds like you're on the right path to solving your problem. It could be the food or it could be seasonal allergies. Is there any sneazing involved? IDK if that would help narrow it down from "stuff in the air/grass" to whether it's the food.
My only experience with scratching was with Sophie. When I first brought her home she would scratch her body (not her face) a lot! I thought it was her shampoo/conditioner. So between myself and her groomer we were forever trying different bath products. Even using the "oatmeal" shampoos and condition. When none of that worked, the only thing left (because it was December and there was no pollen) was the food she was eating. At the time I was feeding Royal Canine.
Although a lot of Yorkie's do well on this food, it was not to be for Sophie. Once I made the switch to a grain free food, her scratching stopped. In addition, her coat improved and her eye goop is very minimal. I have the same results for my two Biewrs.
For Sophie, changing her food was the answer.
Good luck and I hope you figure it out!