Your grades and involvement look good and are comparable to everyone currently at SSM. Don't stress about "Will I get in with what I have or not; is my congressional district real competitive" instead do your best to package your information and if it is meant to be it will happen. Plus you cannot change what district you live in and you cannot change what you've been involved in over the past few years so embrace your set of circumstances.
Spend some time thinking about why you want to go to SSM. What can that school provide that your current school cannot? Why is a residential high school a better option for you? My son came from a school where he could not take AP classes as a sophomore so we really emphasized that deficiency in his essays. Think about what YOU can contribute to the school environment; why are YOU a good candidate. Be forewarned that in previous years some of the responses were limited to 500 characters (yes characters, not words) so you must be very concise.
NCSSM is a RIGOROUS program and should not be taken lightly. Are you willing to leave home at 16/17, be responsible for getting yourself up and to class everyday, organize all of your homework as well as laundry, chores and on-campus work, learn how to live with roommates/hallmates, balance social time and work time, handle most issues with teachers, administrators,etc. without mom or dad's daily input...???
Ask questions, review the website throughly but understand that there is no secret (or public) formula for preparing an application that will definitely get you accepted. If nothing else this will be a great process to get you ready for the college app process.
Best of luck!!!