Really, you don't "need" YC to build your own startup...
This is personal, but I've been running of side projects/webapps that make decent revenue from ads and (in one case) a freemium pricing model.
I'm all of 17 this year and have been doing this for about 4 years now...
YC is only nice because it gives you (1) Lots of investor and public interest via TC and other blog articles. (2) Great advice, tips, and help via pg, harj, jessica, and the rest of the gang as well as the (pretty large now) alumni network of successful YC-funded startups.
YC admits teams that have no product yet to those with several years of experience in their market. It's going to be a bit more competitive now that everyone knows about them plus the whole big-money-addon deal by Yuri Milner, but if you have the skills and believe you have a good MVP to pitch to YC...fly on over to Silicon Valley.
Again, IANAL so there are probably plenty of stake-holders rights things to deal with if you're not of the age of majority and other little things that might be a barrier, but I'm waiting to hear what pg and others with more experience have to say on the matter.
I'm in pretty much the same boat as you, I have been running projects for a while to pay my way through school and I understand that to start a startup we don't NEED YC, the point is we WANT YC onboard.
I have (or will have in a couple of days) another two founders on the small team working on the project and they are both significantly older than me, so hopefully that could help towards solving a few of the legal issues, the question is, would pg/harj/jessica and co. accept a young founder in a team of older founders?