I recommend some Googling, as I vaguely recall that peroxide is a bad idea on broken skin if you want it to heal quickly. Last week I was cutting some bread with my excellent knife specially designed for the purpose and failed to stop when my finger was approaching, thus I can attest that it cuts those very well too. I washed it and put on Polysporin and an adhesive bandage. So very inconvenient and frustrating, but not nearly so dangerous as your experience. Please be very careful, since spinal injuries are no small matter and that stairway sounds lethal.
