When Christian went in to visit with the birds, he saw that Pierre's face was covered in blood, and that blood had splattered all over the hospital cage as well. It was a horrible sight, and poor Pierre was still pushing his beak against the perch, most likely trying to make the pain stop. We cleaned him up in warm water, and could see that he had stropped the live, remaining piece of beak until it pulled away from his jaw and bled. The bleeding stopped and, once clean, we wrapped him in a towel and scratched him until he calmed down. We returned him to his warm cage with the heating pad turned up and he even ate, which was unexpected. For such a tiny, fragile little bird, he's a fairly resilient little bugger.
However, my biggest concern now is that he will repeatedly re-injure the beak until the piece that is left dies as well, and, as our vet doesn't have a call system, we couldn't contact her to ask what we should best do to prevent this from happening tonight. I'm at an utter loss to know how to keep him from hurting himself. He's had such a tough little life so far, I just want to make him happy and contented. I suck at it so far.