The problem you have is that it does indeed look like you could have been racing. You were side by side, then one of you sped up and got in front of the other car. Unfortunately because your case is so ambiguous the only way you're going to get out of it is if you get a lawyer because a county prosecutor or whoever will be there representing the government against you is not going to cut a deal with some kid in a modified car. It also sounds like the cop was influenced into giving you guys tickets because of the cars you were driving.