Hey Timberdad44,
From what we understand, you're experiencing issues with adding and opening Shazam songs in the Apple Music app. First, make sure Media & Apple Music is enabled in Settings > Shazam.
Make sure Music Recognition and Shazam is enabled in iCloud. For more information, click here: Use Shazam on iPhone, iPad, Apple Watch, or Mac. Once there, scroll down to the section labeled "Sync Music Recognition in Control Center with the Shazam App".
If issue persists, close both the Shazam app and the Apple Music app. After doing so, restart your iPhone. Restarting apps have been know to resolve issues.
Also, make sure your iPhone is up-to-date along with the Shazam app: How to manually update apps on your Apple device. Updates include bug fixes.
If those steps do not help, uninstall the Shazam app and then install it again.
Hope this helps. Take care.