Music files show on phone, but not in Music library

I have several artists and albums on my Mac that show in the Music library. I've synced with my phone and if I view files on the phone through my Mac I see the files are on the phone. However, they don't actually show up in my Music library on my iPhone. I've tried restarting and syncing. I update my phone and also restarted my laptop. Nothing seems to work. Best I can tell is that they are all mp3 files from older CDs, but also a recent download through Amazon music after purchase the vinyl album. Is there anything I can do to get these files to appear in my library?