When I went in to check on the reptiles this morning, Sithis had shed. I checked it over and it was complete. He still seems a little congested, but the swelling has gone down some and he seems to feel much better than he did last night.
I think now it was probably unfortunate timing and his mouth got irritated from the dirt right when he was about to shed, and just made everything worse. I'm still going to pick up some hibiclens though, since that just seems like it would be good to have on hand when I need it.