Let's see if we can help you.
You are talking about an iPhone aren't you (and not an Android one)?
Have you previously added music to this specific phone and if so, how? Was it by Manually Managing the phone or by Sync? (They are two quite different procedures.) If you're not sure, connect the phone to iTunes and look on the Devices/Settings/Summary tab, for the Manually manage music and videos option. Is it ticked (checked) or not?
If it is not ticked, switch to the Device/Settings/Music tab, which is just below the Settings/Summary option in the left hand panel. Using the screenshot below as your guide, is Sync Music ticked (checked) and if so, which of the options below it is selected, Entire music library or Selected playlists, artists, albums and genres?
Once we have the answers to these questions, we can probably sort out what you need to do.