Hey there DavidKnoxLB,
Thanks for reaching out to Apple Support Communities. We understand you’re having issues adding music to your library. We’ll be happy to help with this.
It sounds like this issue is intermittent but happens often enough. Have you tried restarting or force closing the apps for this issue? If not, try both steps:
How to force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone
It’s a good idea to make sure your iPhone is up to date and has plenty of storage as well:
Update your iPhone, iPad, or iPod touch
How to check the storage on your iPhone, iPad, and iPod touch
Then try adding music once more and see if the issue is resolved.
Add and download music from Apple Music
We hope this helps.
Take care.