I've actually had happen something similar happen with my male Lesser in the past, not with teeth protruding through the upperlip (ouch!), but he managed to get his bottom teeth hooked around outside of the upperlip and couldn't open his mouth. It looked a lot worse than it actually was, thought he had broken his jaw at first, but I was able to him undone myself with a plastic toothpick in the end!
So glad it wasn't anything this bad though and I hope you guys have a speedy recovery. ^^