Is it possible to add music to your Music Library on the iPhone?
This is currently impossible. You can share downloaded audio with many apps - Dropbox, Google Drive, or the one I use most often for learning music and the like, forScore. But you can't share it with iTunes. Although, songs purchased on your phone can easily (or automatically) added to the libraries of your other Apple devices via Settings - iTunes &amp; App Store and selecting Music under Automatic Downloads.