Thank you for using Apple Support Communities. It's my understanding you have duplicate songs on your iPhone after syncing with iTunes. I'm happy to help.
It's possible the songs were duplicated in iTunes and have now synced to your iPhone. Please follow the steps in the link below to remove duplicates from iTunes then sync again:
Find and remove duplicate items in your iTunes Library
Also, with Apple Music you can use iCloud Music Library to access your music library on all devices signed in with your Apple ID without having to connect with iTunes.
Turn on iCloud Music Library
Have a wonderful day!