Thumb drive is not appearing on desktop after plugged in.

Try another Thumb/Flash Drive.

Go to Finder > Preferences > make sure "External disks" is checked.

Sounds silly, but wiggle it. Mine often are not recognized but wiggling them in the port coupled with reinsertions usually works.

It's for this very reason I bought a couple of PNY 250GB SSDs for transferring data. They are less than $30US (Amazon) and they've been flawless for the year or so I've had them.