Hi Magic_7,
Thank you for using the Apple Support Communities! As noted in the resource below “Your Apple ID should not be shared with anyone else. It provides access to personal information including contacts, photos, device backups, and more. Sharing your Apple ID with someone else means you are giving them access to all your personal content and may lead to confusion over who actually owns the account. To share purchases, photos, a calendar, and more with someone else, try Family Sharing, iCloud Photo Sharing, or other easy-to-use sharing features.”:
Apple ID FAQ
Regarding resolving the behavior, let's open the Apple Music app > Tap Profile > Account Settings (at the bottom), do you see your Apple ID there? If not, we'll want to ensure that your Apple ID is showing in Settings > Tap Account. If you don't see your account listed there, you'll want to sign out and log in using your information and the steps here, which also goes over what to expect when performing these steps: Sign out of iCloud on your iPhone, iPad, Apple TV, or Mac - Apple Support
If it appears that all of your data is correct, reach out to Apple directly for a deeper look: Get Support
Hope this helps!
Have a great day.