TheLittles Said:
"I went to the beach and couldn't get my phone to play music on Apple Music. I've since then downloaded music to my library. I just want music to automatically play from my library when there is no service"
-------
Playing Music with no service:
A. Home Music would play just fine in a third-party app. As for iTunes Store purchases, you need service, if no WiFi is available.
B. "No Service":
Looking on the top-left corner on your screenshot, does it show "No Service"? If so, so see this link, for more on troubleshooting this: If you See No Service or Searching on your iPhone or iPad - Apple Support
C. Have you Relocated?:
Have you are now living in a different country/region, then you need to zero-out your balance. Then, all should be modifiable. If you are just visiting someone, however, then let things be. If you were to change it, then all would be lost. Purchases need to be repurchased in order to use them in a different country/region. this all has to do with licenses between Apple and the Studio or Developer.