First -- are you saying that the 14 albums you mentioned were moved from the PC to the phone already using Windows File Explorer? If so, do you recall how you moved those music files? Did you just drag and drop them from the PC's hard drive to the "Phone" listing, or did you try to drag and drop them directly into a specific folder in the Phone's storage?
Second -- Google Play Music is its own app. On a phone, you can't access it from the browser (unless you have the browser set to "Show Desktop Site," which I'm guessing you don't). So do you mean that you're opening your App Drawer and then tapping the Google Play Music icon to open the Google Play Music app?
Third -- Remember that Google Play Music will show music that's locally saved to the phone, but also music that's in your Google Play Music "locker" in the cloud (which is where you'd find music you purchased in the Play Store or music you uploaded from your computer to the cloud). If you go to music.google.com on your computer browser, do you see those 14 albums there as well? If so, then you most likely won't find those music tracks saved locally on the phone. (With Google Play Music, you can download music tracks for offline listening, but those actual files will be in a protected system directory that the user can't access with a file manager.)
Fourth -- If you're sure that you used Windows File Explorer to move music files from the PC to the phone at some point, then use a file manager app on the phone (Samsung's My Files app, or a good 3rd party one like Files by Google or Total Commander) and explore the phone's storage. Don't just tap the Music category -- on a lot of file explorers these days, the main screen will have categories like Music, Photos, Documents, etc. that shows all of those kinds of files that are stored anywhere on the phone, and that the file explorer groups together for convenience. But it can be difficult to determine what actual folder each file is in. So look in the file explorer app for an option to Explore, meaning that you're looking through the actual folder structure of the phone's storage. The first folders/directories to check would be /Download, /Music, or the main "root" directory for the user.