Q: Ipod shuffle not showing in itunes

See here: iPod shuffle (4th generation): Not seen in iTunes

I assume you are using the dock connector cable that came with the iPod correct?  Has iTunes ever been able to successfully see your Shuffle or is this the first time you are connecting it to this computer?

Make sure you are plugging the Shuffle to a high powered USB 2.0 port. It wouldn't hurt to remove all other connected USB devices with the exception of your keyboard and mouse if applicable.  Then reboot your PC and reset your shuffle using the provided instructions in this link.

Resetting iPod shuffle

Then open iTunes and reconnecting your iPod to see if that helps.

B-rock