Q: Icons next to each song in My Music

Hi cheekyage,

I understand that you have some questions about the music that was synced to your iPhone. I can answer those questions for you. 

So what it is asking you is If you want to delete the song from your music library or if you just want to remove the download from your iPhone but still keep the track so it can be streamed. So that prompt that you are seeing looks to be in relation to Apple Music.

Apple Music will use what is called iCloud Music Library. This would keep everything in sync for you. It would even let you see your entire iTunes library that is on your computer, show up on your iPhone. Then you would not need to sync and could just access your music and play it. Take a look at the first article below to go over how to enable iCloud Music library across all your devices. 

Sync Apple Music across your iPhone, iPad, iPod touch and computer
https://support.apple.com/en-us/HT204926

Take a look a the few articles below that go over using Apple Music within the Music app and then about deleting music form your iPhone or from your Music library. 

Use Apple Music in the Music app
https://support.apple.com/en-us/HT204951

Delete songs and music videos from your iCloud Music Library
https://support.apple.com/en-us/HT201323

Delete music, movies, apps, and other content from your iPhone, iPad, or iPod touch
https://support.apple.com/en-al/HT204343​

Have a good day

Hey cheekyage,

It was no problem at all. If you any other questions that need answering, feel free to post a new one and we will get to you as soon as we can. 

Take it easy