Any food that has corn in it can make your dog itchy and it can cause food allergies. There are some excellent foods out there...Science Diet would not be one of my picks. Innova, Wellness, Canidae and Nature's Variety stick out in my mind right now but there are lots of others too. Here is a website where you can take a look at the better foods available, they're rated by stars, the 5 star foods are within the right protein levels for a Yorkie but the 6 star foods are too high in protein. Here's the website:
http://www.dogfoodanalysis.com
Click on the link at the bottom and it will take you to the list.
We use Nature's Variety raw diet, I know it's not for everyone but they also have dry kibble, here is their website:
www.naturesvariety.com I have noticed some big improvements in my boyz since switching them to NV so we're sticking with that and home made food.
Good luck finding a food that will work for your baby. Oh...also...when you bathe her make sure you get all of the shampoo out, rinse, rinse and rinse again...soap residue can also make them itchy.