Hello 77Clemson,
If all of the songs needed on the iPhone are being synced by the Mac (or purchased from the iTunes Store) then you may try reinstalling the Music app on the iPhone.
As part of the process when uninstalling the Music app from the iPhone this will delete the associated data from the device, which will include the songs that were synced over. Then, try re-syncing the iPhone with your Mac.
Remove apps from iPhone - Apple Support
Remove apps
Do any of the following:
• Remove an app from the Home Screen: Touch and hold the app on the Home Screen, tap Remove App, then tap Remove from Home Screen to keep it in App Library, or tap Delete App to delete it from iPhone.
• Delete an app from App Library and Home Screen: Touch and hold the app in App Library, tap Delete App, then tap Delete. (See Find your apps in App Library.)
If you wish to note re-download the app you may also try heading to Settings > General > iPhone Storage > Music, and then tap Edit above the 'All Songs' section, which will let you tap on the (-) icon to delete all songs that are downloaded to the device.
Cheers.