Half halts aren't everything. Just because you give a half halt, if the rest of your body is not corresponding with the aids of what you want her to do, it's useless. For example, if you throw your weight forward but half halt for your horse to slow down, it makes it very hard for the horse to know what you are asking for.
At the trot, do not half halt every time you post. This will only make your horse numb to it and she will start to ignore it. Instead, sit tall and slow your posting down. Your horse will have to slow to match it. Half halt in the corners or whenever you feel your horse is starting to speed up, but make sure you're not bumping/squeezing with your legs or tipping forwards. Don't send mixed messages.
You also need to learn to sit deep and back into the saddle while approaching a jump. This enables your horse to gage the distance and get proper striding, while encouraging her not to over jump. Don't get into 2-point too early, and don't let her take off from far away. Hold her back until you're close enough to the jump. And make sure you wait for her to take off and do not over jump.
Videos and pictures would be nice. Could you post some?