Hello Tina_0! Thank you for participating in the Apple Support Communities.
We understand that you’re unable to add songs to your Apple Music library, even though it says those songs are being added. We'd like to look into this with you to see how we can help.
Let’s try the following steps to see if they help, and test after each step:
• Restart the Apple Music app: Apps > Settings > Apps > Apple Music > Force Stop. Return to the Home Screen or application list, and reopen Apple Music.
• Clear the App cache: Apps > Settings> Apps > Apple Music > Storage > Clear Cache. Return to the Home Screen or application list, and reopen Apple Music.
• Restart your Android device.
• Sign out of Apple Music and then sign back in. Open the Apple Music app, tap Library, then tap the menu button. Tap Account Settings > Sign out. Sign back in by tapping the menu button > Settings> Sign in. Any music that was downloaded for offline listening will need to be downloaded again after this step.
Make it a great day!