If you are not seeing your full list of iTunes songs when you launch the music player, it's possible that some of your songs are not downloaded to your phone. Try these steps:
1. Open the iTunes Store app, then select More.
2. Tap Purchased > Music > Not On This iPhone.
3. Tap Recent Purchases > Download All (or select which ones you want to download).
Keep in mind that your music must be located in your iTunes account, not the cloud, in order to play it in the app.