a) worst injuries due to falls my kids have had was when they were trying not to hurt other skaters who were crossing right of way or jumping carelessly. Sadly, the other kids now get out of the way and watch for my kid who is the biggest, strongest and most powerful jumper on the ice: they're scared of getting hit, so they watch out. thus, their fear is making them more cautious and careful.
b) if you are really nervous about falling, try some martial art or gymastic training. In martial arts in particular, you are taught how to fall so as not to injure yourself, and how to use your own momentum to "roll up" back on to your feet without a jarring stop. Years of martial arts training has paid off in terms of minimizing injuries on falls, and in removing the "fear of falling". I would suggest aikido, something like that where you are throwing or being thrown.