Q: I can't listen to music through headphones on my iPhone

Have you tested another set of headphones? Have you checked the volume setting for the headphones? What troubleshooting have you tried?

If you have tried another set of headphones and cannot hear, then there could be something wrong with the jack. Since you also mention the ear piece area. You can see this regarding that for some hints, but you may have to have the device looked at for hardware errors. If you can't hear a person on a call or voicemail or if the sound quality is poor on iPhone - Apple Support

If you have followed that article, including restoring the device and still are having problems hearing, then you need to have the device serviced.

You're welcome.