I had no clue they shed their tongues either!

I don't know a huge amount about garter anatomy, but a lot of animals have glands in the neck just below the jaw. The first thing I thought of when I saw his neck was a swollen lymph node... When I've seen that in other animals it's sometimes because the gland itself is infected, or sometimes due to an infection nearby (like if his mouth was still infected or something?).
Don't know if that's helpful, but it's one of the only times I've seen swelling on just one side of an animal's neck.

Hope your snake gets better..