I am so very sorry that you hit the ice. I know that hurts. I can only imagine how embarrasing it was.... How is your knee?
It is really hard to present oneself as a serious professional when you bust your bootie and are bleeding all over the ice. It takes a "big" person to be able to laugh at one's self. I hope your students appreciate you .... sounds like you go way above the call of duty. You need a TEACHING MEDAL OF HONOR for our fallen teachers (most especially for those who fall and get up to try again).
Sending get well wishes and hugs