I wanted to give you all an update.
I tried a few times to pull it out of him with no success. In fact, I'm afraid I traumatized the poor guy, because when I tugged really hard, some clear liquid came from his face. I think he vomited. Since I couldn't remove it without further hurting him, I froze him, got an art knife, and did an exploratory surgery.
I still don't know what it is, but I believe it's part of his regular anatomy. When I cut him open, I found a second one on the other side in the corresponding spot, like how we have ears on both sides. The second one, however, wasn't outside of the shell.
My best guess is he got injured and part of him slipped out like a hernia of sorts but I have no real confirmation.