Lizzy - as the others have said - you have made a common mistake.
If you are learning to drive, then you'll pick something not too fast and a little dull, but you have to learn on something steady. You mustn't buy a sports car to learn on.
Now that 22 y/old can show you a thing or two, but first you have to learn how to sit quietly on it, and not excite it. You probably touched an accelerator inadvertently. Well done for getting back on.
The best thing is for you to go back to that school horse and ask the tutor to explain how to get it to canter. You'll find that most school horses are a bit lazy and even if they will canter, they don't go fast even if you kick them in the ribs.
Teaching someone to ride is a skilled job, your mates and your family aren't always the best folks to teach, even though they know how to ride themselves. Try again (and you don't have to canter until you know how to work the brakes).
PS You were wearing a riding hat - weren't you!