Also, I'm going to venture a guess that perhaps your horse didn't 'bolt'? A bolt is when your horse shoots off at a fast gallop. Sounds like he was a little unbalanced with the downhill slope and broke into a canter since he wasn't balanced enough to just trot down (very common with a green horse). Even still, this is terrifying for someone who isn't ready for it. When people start riding their first instinct to fear is to lean forward, even throw themselves at their horse's neck. Unfortunately this will only make your horse go faster! As someone said (myboypuck?), you MUST SIT BACK!! Or at least sit up and then get your reins again. It's the opposite of your instincts, but you must do it! I am a huge huge fan of the one rein stop, but it's hard for beginners to learn properly (ESP from a canter) so I wouldn't recommend it yet (if you hold your hand up too high you can flip your horse over) as you must be completely centered in the saddle, be able to stretch up, and be secure as you crank your horse's head to the side. If your horse was a bolter, then yes, maybe you should take the time to learn it properly. But not easy for everyone.
But like I said, find a new barn! Your parents might think you're a chicken at first but believe me, if you continue at this barn you could get seriously hurt and you will lose your confidence altogether. If you go somewhere with proper responsible instruction and solid horses, you will wow your parents one day with your great riding skills!