Not to be nit-picky, but middle class incomes would not support paying tuition+board at a place like Lville ($73K per year). Most of the students at Lville are not middle class. There are certainly many students who attend that receive financial aid though.
Just make sure you have a conversation with your parents about finances. As a child, you might not be familiar with how much your parents make per year.
I would suggest sitting for the next SSAT, even if its after the Jan 15 deadline. It can help in case you are waitlisted. Or if the scores are higher, you can submit even up until the March 10 decision date.