Carrying a whip could be useful, but it won't get rid of the problem. You need to get at the colts owners and talk to the BO. Apologizing won't do anything. The colt could seriously injure you or your horse. If nothing can be done, get out of there. It's not worth the risk.
The baby is just being a baby.......with no discipline and training, but I doubt he is "mean" and trying to hurt anyone on purpose. BUT, YES, he could actually kill or injure someone if this continues on.
My yearling was the same way and he was gelded at 5 months and worked with pretty much daily. Yeah, he was my first foal and we had discipline issues, but he actually outgrew this behavior. It used to be every time I brought his momma back from riding it was play time and I could scarcely get her in the corral safely. He would immediately start climbing on her and biting her and wanting to play. I would smack a whip or a rope at him and he would just run around to the other side and continue his torment. Gosh am I glad he outgrew that!
But anyway, it is definitely dangerous. He actually climbed up on the horse I was riding one time and ponying him (not his momma but another gelding). Not good.
I guess what I'm saying is, he is being a bratty baby but it is not your responsibility to train him and you and your horse shouldn't have to be at high risk of injury because of a baby that's not even yours. I don't know what the answer is, but you should not have to deal with it. A stray hoof could hit you in the head and kill you. (Wearing a helmet in the pasture to retrieve your horse would be a good idea).
If they won't separate either the colt or your horse you might have to move.
Jumping on him ? That could be mounting, which a horse will do to prove dominance. It is very dangerous, can fx your sr horses shoulders, hips. Plus can cause harm to you. IF the barn owner does not move this colt to another pasture, and only offers an apology or an excuse, I would look for another boarding facility. The owner obviously does not take your safety or your horses safety into consideration. Guess the money for two horses, out weighs you .