Hello Mary-Ellen, and thank you for choosing JUSTANSWER.com
DO you have iTunes?
To get songs onto yoru iPod, you must first get them onto yoru iTunes, THEN you can transfer them to your iPod.
To add songs, albums and playlists from Apple Music to My Music, make sure to turn on iCloud Music Library on your device.
Then see the instructions seen below in the image link:
You must use the SAME iCloud account on the iTunes, as you are using on the iPod.
That is how the music you purchased is verified.
When you made the purchase you were logged into a iCloud or Apple account, and that same account must be logged into on your iTunes, and iPod, to be able to add the songs TO your iPod.