HI there, welcome to Yorkie Talk and congratulations on your new addition - what a beautiful family
As far as eating goes, it seems that a lot of Yorkies are picky eaters. Mine certainly was when we brought her home. The magic trick for me, was to pour the tiniest bit of water on her food, then put it in the microwave for 10 seconds. She devours it every time.
Let us know what your vet says, it also sounds to me like she may have kennel cough, which is very treatable.