You may indeed lose some potential, I'm not sure. Ask your coach. I guess you have to weigh up the importance of beating a few other people right now against the possibility of doing yourself long term damage and being out of competition altogether a few years down the line due to not taking enough time out now. And perhaps even being out of running altogether too. You don't need to catch these other kids, you want to. There is a difference you know.
At the end of the day though, it's your call as to how you want to play it. Are you going to to plan for the long term or the short term? Lots of young athletes take a long period off and return to the top of their game. Lots don't. Lots of people run through injury and don't seem to adversely affect their long term ability. Lots will try it and end up doing themselves real harm. You might never catch these other kids even without your current injuries.
In a kind of 'sell your soul to the devil' scenario, if you could run at national level - and win - but knew you'd be spending the next few years in leg braces and crutches, would you do it? I suspect a lot of people possibly would...
Good luck with your recovery. I'm working my way through shin problems at the moment too. Though I DO just run for fun.
Someone on here recommended toe tapping exercises which I have just recently started. Have you heard of them? Search 'toe tapping shin splints' on youtube.