I figured it out. In case anyone else has a setup similar to mine and wants to do this, all you have to do is make sure that the file locations on both computers are the same. To change or confirm the file locations, in OneNote click File > Options > Save & Backup.
I then use the free Syncback (http://www.2brightsparks.com/freeware/)
to sync the files between computers.
Works the same way as my other Office data files!
That was a lot easier than I thought!