Hi there HWinNY,
We'd like to help, but we need more details to understand what's happening.
What exactly happens when you try to set a song you downloaded from Apple Music as an alarm tone? The more details you provided the better equipped we'll be to assist.
As you have a compatible model, the latest version is iOS 15.1. You can verify this within Settings > General > About. Here's a link that'll show how to first back up, then Update your iPhone, iPad, or iPod touch.
Has a restart been tried? This link shows How to manually update apps on your Apple device.
Cheers!