This seems to be a common thing. From the web page of an attorney:
It is common for motorists to go to traffic court and express their surprise when the judge tells them they have to hire a lawyer. It is not just common. It is a daily occurrence. The reason that courts want the defendant to be represented by counsel is courts want to preserve the right to sentence the offender to jail.
There is no better example of how traffic court has changed in recent times than the incidence of jail sentences for these tickets. Most lawyers who do defense work were waiting, observing how traffic court judges would handle these speeding tickets under the new law and media scrutiny. And suddenly, defendants got sentenced to jail in Cook County and DuPage County.
Court reporters suddenly were ordered to take records of the proceedings in field courts where, up until that point, no one had ever gone to jail.
So, the best advice for getting a ticket for speeding this fast is simple. Hire a good attorney.
The attorney of course has an interest in getting people to hire him. But it sounds like your best course is to sell your car and use the money to hire an attorney. Even if you get hit with a suspension instead of jail time, you won't be driving for a while. David Siegel pointed you at the public defender's office, but an attorney you are paying for is likely to do a better job than a PD.
In the meantime write a statement about any mitigating circumstances that might help reduce the severity of your sentence. DO NOT LIE. For instance:
Was there a good reason you were driving, and/or in an unusual hurry, like a family emergency?
Are you still at school or college, or other education or training? Would jail disrupt this? Likewise a job.
Have you done any volunteering, church, or other activities that put you in a good light?
You don't say how old you are, but I'm guessing young from the fact that you hadn't got your license "yet". If you were under 18 when the offence occured this is likely to help. Also, can you get your parents into court with you? Can you say that you come from a good home and they take this really seriously? Evidence of a concerned and supportive family can help.
Any other adults, preferably not relatives, who can testify to your good character?
Have you been in trouble with the law before? How was your school discipline record? If you can show that you are normally law-abiding and this was exceptional behaviour that can also help.
Don't forget to say how sorry you are, and how you promise to learn from this mistake and do better in the future.
(Edit: The above assumes you are pleading guilty. If you plan to contest the charge then you really need a lawyer.)