Can I add my own music to Apple Music on iPhone?

You can manually synchronize purchased music (from your own CDs, the iTunes Store, etc.) from your computer to your iPhone.

Sync your iPhone, iPad, or iPod using your computer - Apple Support

If you are a subscriber to Apple Music or to iTunes Match, you can use Sync Library

Use Sync Library with your Apple Music subscription - Apple Support

However, I believe that the Sync Library feature may synchronize DRMed versions of your purchased songs to your other devices.