Hello richardfromhixson,
We would like to see how we can help you ith your missing iTunes library. It will not be possible to transfer your music from your iPhone to iTunes, only iTunes to iPhone. Are you able to find the missing library with the steps in this link: Back up and restore your iTunes library on your PC - Apple Support
"Find the iTunes Media folder
By default, your iTunes Media folder is in your iTunes folder. To find it, go to User > Music > iTunes > iTunes Media.
If you don't see your iTunes Media folder in the above location, here's how to find it:
- Open iTunes.
- From the menu bar at the top of the iTunes window, choose Edit > Preferences.
- Click the Advanced tab.
- Look in the box under "iTunes Media folder location" for the location of your iTunes Media folder."
Cheers!