Keep my music on my phone but not in iTunes
This may be possible by configuring iTunes to Manually manage music and videos. Then iTunes shouldn’t require you to have the same songs on your iPhone as you do on your computer.

Another way is to enable iCloud Music Library. This is a paid service that becomes available if you use either iTunes Match ($24.99/year) or MUSIC ($9.99/month).

By now you should have been bombarded with prompts for MUSIC. To subscribe to iTunes Match, open iTunes and open Music → Store, then click iTunes Match on the right hand side:



Your iPhone will then sync music with iCloud rather than with iTunes on your computer, and you will no longer need to keep any music on your computer. In fact this makes your entire music library available for streaming so you don’t even need to keep it on your iPhone either.