Here are a couple things to check.
1. First in the app, in the upper left hand corner, does it say "on device"? If so tap it and select "all music".
2. Click your menu button and select refresh.
3. If that doesn't work, go to your device settings and select apps, applications and you will see downloaded at the top of the page. Find Google Play Music app and select it. Then on the next page click "Clear Data." Next click OK on the pop up window. Then go back to the Play Music app, and set it back up.