that 'thing' has never worked for me or anyone I know.
if you're a teenage driver, your insurance is probably already as high as it's going to get, unless your dad got you some kind of deal. I doubt they'll drop you for a ticket, or even have that much room to raise your rate (I'd assume 25-50$ more a month or so).
if you dont want to go to court and fight your case then be prepared to suffer the consequences. My advice would be to definetly go to court, whether you plead guilty or not. This probably won't be your last ticket and getting an idea of how the whole system works may really save your ass in the future.
Feeling sick is not an excuse for speeding; none of the things you've mentioned would convince a judge that you were wrongly cited for speeding. The judge wont care about the other cars, your friends, your feelings, or how shitty your day was.
The officer should have mentioned a driving safety course to you - if you sit through the 8 hour course (give up a saturday), your ticket will be cleared from your record, and your insurance CANNOT be raised (by law in many states). This is what I would recommend for you, if it is possible. You were speeding, you are young; any excuses you try to come up with, or anything you believe to be 'unfair' will be looked down upon by a judge. I think that your best bet is to take it like a man and get into a driver's safety/training course to get the ticket cleared.