home sharing libary!?!?!?!

Things to check:

Are you in fact on the same network as the computer(s) hosting your library?

Is iTunes running on the host computer(s)?

Are you in fact signed onto the same iTunes account (Apple ID) on the iPhone and the host computer(s)?

What do you see in the Music app when you select "..." at the bottom of the screen and Shared in the list?

OK, that answers my last question. What about the others? Are you on the same network and iTunes account and the computer(s) running iTunes?

Is any of the music in iTunes on the computers bought from the iTunes Store, or is it all third-party music? If you have bought any music at all from the iTunes Store with the current account, it should be available for download in the Music app. (At least, I think so. I have iTunes Match, so our cases may not be the same.)

Also, do you have "Show All Music" active (green) in Settings > Music? That would suppress display of music available for download but not on the phone.

At this point, I'm just trying to determine why you have a black screen in the Music app with only an offer to go to the iTunes Store and no other options, as if it thought you had no access to any music.