Hi christalt,
I understand that you are attempting to sync your iPod shuffle, but you're being told it's paired with another library. I know that it's important to have up to date content available on your iPod, so I'm happy to provide some direction to help with this.
The message that you are describing explains that you've already synced your iPod with another iTunes library. This means that in order to sync with this one, it will need to first remove the music from it. If all of your music was purchased from iTunes, this should be no problem, you'll simply need to redownload those songs or transfer them from your iPod:
Redownload or transfer your iTunes Store purchases from an iPhone, iPad, or iPod to a computer - Apple Support
Redownload your purchases
Sign in to iTunes on your computer with the Apple ID that you used when you bought the items on your iPhone, iPad, or iPod and download your past purchases.
You can also transfer your purchases from your device to your computer using iTunes.
Transfer your purchases
Before you transfer your purchases, make sure that your computer is authorized with the same Apple ID you used to make the purchases. Learn how to authorize your computer using iTunes.
If the content that you want to transfer was purchased using multiple Apple IDs, you'll need to authorize your computer for each one.
To transfer purchases from your device to a computer, follow these steps:
- Connect your device to the computer. Wait for its icon to appear in the upper-left corner of iTunes.

- From the menu bar at the top of your computer screen or at the top of the iTunes window, choose File > Devices > Transfer Purchases from "[device name]".
If you’re using Windows and can’t see the menu bar, learn how to turn it on.
This feature works only for content purchased from the iTunes Store. Any items that you import from audio CDs or receive from other sources won't transfer from your device to the iTunes library. However, all podcasts from your device's Podcasts app and copies of all PDFs, books, and audiobooks from your device's iBooks app will transfer to your computer. Learn how to transfer media to your iTunes library.
Once you've confirmed that all of your music is in this iTunes library, you can sync again adding back any music that was removed that you wish to still have access to.
Thanks for using the Apple Support Communities, cheers!