Hey there JulietteN65,
Thanks for reaching out to Apple Support Communities. I understand you’re having issues using Apple Music as expected on your iPhone. I’ll be happy to help.
I know you mentioned recently updating iOS. Just to be sure, the latest version is 13.4.1, not 13.4. If you haven’t already, install the latest update and try again.
If that doesn’t help, force close the Music app on your iPhone and then go to Settings > Music and turn off Sync Library and Show Apple Music. Just as a heads up, that last step will remove any songs you’ve downloaded to your iPhone and you’ll need to download them again. From there, go to Settings > Your Name > iTunes & App Stores and tap on your Apple ID, then Sign Out. After successfully signing out, delete the Music app and restart your iPhone:
Restart your iPhone
Sign back into iTunes & App Store settings, download the Music app, and turn on Sync Library and Show Apple Music. Try using your Music app and see if the issue is resolved.
Regards.