RC can cause itching...I use to feed RC but one of my yorkies itched so bad so I changed their food. I feed now Canidea and so far so good!
I have found quite a few yorkies do have sensitive stomachs and you can feed one type of food for a long time and they "CAN" develop allergies to that certain food. I would try and find a food they can eat. I have always heard it's good to change their food ever so often but make sure it's a very high quality food. I try and stay away from any kind of grains or corn if I have a yorkie with sensitive stomachs. I've even tried RAW and fed for awhile and a couple of my yorkies couldn't handle it...threw up and wouldn't eat it.
If your vet doesn't have any recommendations then I might would try and find another vet...JMO of course
Donna Bird
Brooklynn's Yorkshire Terriers