Are you pulling on the reins and gripping with your legs, and tipping forward at the same time? Or pulling on the reins in a steady motion allowing the horse to 'lock' onto the pressure?
Some horses will lean into the bit and run through it when you pull, but as soon as you give the rein they will slow.
I certainly wouldn't be jumping this horse. Start at walk, establish breaks at walk, then trot and so on.
Stay on curved lines and circles, and don't spend more than 12 strides in one gait or tempo.