Hi B.. Welcome to MP. Maybe you could sue, but I don't think you should and I think the liklihood of success is slim. I will assume this is a real question and give a real answer (first questions that seem to want to elicit strong responses are often suspicious). I am a lawyer, although I haven't practiced law for years. You would need to file your suit in small claims court (assuming it was a regular break and not something more serious that required surgery, long term therapy, etc.) and you would have court filing fees to pay and paperwork to prepare. Then you would need to prove that the boy either intended to hurt your son or was so negligent he should have known he could hurt your son. How old are the boys? That is a factor. Do you have any witnesses or other information about how it happened? Did your son willingly participate in the race and did he also do any sort of pushing or jostling?
A court is likely to find this was just a childhood incident and no one is legally liable. I'll give you a real life example. Years ago I was involved in a lawsuit in which a teenage girl was very seriously injured at a ski resort and could have died. She was standing at the bottom of the hill and a teenage boy came racing down the hill and hit her. She flew into a ski rack, ruptured her spleen and broke a small bone in her back. She spent weeks in the hospital, missed a lot of school, was in therapy and chronic pain months later and had to give up her horseback riding activities. Her parents sued for the thousands in medical bills they had incurred and for her pain and suffering. There were witnesses that testified the boy was "bombing the hill" (going straight down as fast as he could without turns or slowing down). They lost. The jury said it was just an unfortunate accident and the girl should've known accidents like this could happen at a ski resort.
I am in favor of lawsuits in the appropriate situation since my husband is a trial lawyer and defending lawsuits is how he makes his living. However, this isn't that situation. I hope your son makes a full and fast recovery.