Hi,
In iTunes Right click on the song or remove it from the playlist.
First off you should always back up your music and these devices really don't hold that much. You should start iTunes and connect the iPod. Does your iTunes recognize the shuffle? If so you need to be sure the current OS update is installed. If that doesn't work you will need to reset it. Both functions will wipe all of the songs you have on it but should resolve your issue.