Hi Mrsjensmum,
Welcome to the Apple Support Communities!
I understand that while your iPod nano is connected to iTunes, you are able to see and listen to all of your music on the iPod, but once it is disconnected the iPod seems to be empty. If this is the case, I would suggest connecting your iPod to iTunes and removing all of your synced music and playlists. Do this only if you are sure your music is available in the iTunes library on your computer.
Complete this process by unselecting the Sync Music box and then choosing Apply in the lower right hand corner. Once iTunes has finished syncing and removing that content, I would suggest re-selecting the Sync Music box and choosing the content you would like back on your iPod. Select Apply again when you are ready to sync the content back on to your iPod. The attached article below outlines the syncing process as well.
Sync your iPhone, iPad, and iPod with iTunes using USB - Apple Support
Best regards