Coconut oil can help soothe broken skin. She can eat it, or you can rub it directly on to the skin. Whatever shampoo you use, just make sure to rinse it all of. Sometimes, if you don't, that can cause trouble too. You're also going to get a lot of different suggestions for shampoos. That's why I love this site!
Anyway, I use and absolutely love Yorkie Splash and Shine. Keeps my pup clean and fresh for days, and the smell isn't so overpowering that it gives me migraines. The shampoo looks like water, which turns some people off. The Sheen detangling spray is amazing as well.
When I'm in a pinch and run out of shampoo, I pop on over to Petco and get some Nootie. I'm a little disappointed that it has no conditioner, but it cleans and freshens my pup really well.