Am I pushing myself too hard?

Silly question ahead! So I’ve started figure skating two months ago. Last time I took a hard fall on my knees, because I accidentally put my toothpick in the ice whilst doing crossovers. Mentally held me back for a week. Yesterday I fell on my tailbone whilst practicing a two foot spin. Both of those times someone had to pick me up because I couldn’t immediately get up from the pain. I’ve always been a daredevil. I’m ambitious, but I feel like I’m the only one taking such hard falls. Especially in two weeks time. I try almost everything out my coach tells me to without any doubt. I always thought figure skating was about having no fear. Taking those two falls, thinking about my health and how I’m one of the only ones having to get picked up, I was wondering if maybe I’m pushing myself too hard. (Yes, really.) I want to learn as much as possible as fast as possible, because it’s fun to learn new things. Maybe I should take some private lessons so I’m advised purely on stuff I’m surely ready for? Maybe I should get some more protection? I’m now only wearing knee protection. Or am I really pushing myself too hard?