HOLD YOUR HORSES! (From personal experience of someone I know)
Do not pay the fine. By paying the fine, you are admitting guilt and you will be given a misdemeanor- a CRIMINAL charge (not just a traffic one).
Hire a lawyer who SPECIALIZES in these types of cases. Google/lawyer reviews are your friend.
Have the lawyer put you through a speed calibration test and online traffic school to show the judge you are serious about this case. Some may even like to see your academic record (if you have good grades, I know it seems irrelevant but it is relevant to the judge).
Only after you go to trial and the final decision is made, should you notify your school. The American legal system says that you are innocent until proven guilty and that's the situation that you are in. By informing the school early, you are telling them something without all of the facts decided, and because faculty is also human, whether they should or shouldn't, they will perceive you in a certain light afterwards.
I hope you read this before you do anything that's hard to backtrack from.