When you ride have someone who knows what they are doing watch you. You may feel like you don't need a trainer now, but you will soon. I can tell you are scared of your horse doing this again, this anexiety will only make things worse. When I break a horse I personally don't start off with a bit. I take 2 chain leadropes, I put one over ther horses nose and the other under the horses chin. But in your case I wouldn't do that. Mustangs and Halflingers are known to be bullheaded and to be pushy. I have a half halflinger of my own and I wouldn't be caught dead riding him without a curb bit he pulls thro everything else.
Actually halflingers are excellent jumpers. My half halflinger taught children to jump for 2 years in pony club. There are many excellent successful halflingers that jump.
Start off small. Don't push. Wait till you feel the horse is /ready/ to trot. If you have only only walk for a week then do it. I would never trot a green horse untill I have full controll at the walk. And I would never canter a horse untill I have full control at the trot. Especially with Halflingers its hard to get thro to their heads. They are stubborn. You give them an inch and they will take a mile. This horse already knows it can get away with what it did. Chances are it will do it again. Don't just get off when your horse does something bad. It WILL learn that if it scares you enough you will get off. My pony learned that at the age of 2. He is 9 now and till this day he spooks for kicks to try to get you scared. Get a trainer, or someone who knows what they are doing to help you.