Thanks for reaching out to the Apple Support Communities, alicja52!
It sounds like you are having an issue with not being able to play Apple Music. First, I recommend checking out this article with steps for How to force an app to close on your iPhone, iPad, or iPod touch and quit the Music app. Once it’s closed, Restart your iPhone, iPad, or iPod touch and test to see if the issues are still going on.
If they are still going on, check out this article to sign out and then Sign in to the iTunes Store on your iPhone, iPad, iPod touch, Mac, PC, or Apple TV. This step will temporarily remove any music you’ve saved for offline listening, so you will have to redownload all the music saved for offline manually again. Also, be sure you go to Settings > Music and turn on iCloud Music Library if you're using iOS 12. If you've upgraded to iOS 13 the iCloud Music Library is now Sync Library when you go to Settings > Music.
Let me know the results and have a great day!