When you pay a ticket by mail, that is an admission. If you don't want the points, you need to hire a criminal defense attorney in your area to locate the case, redocket it, and see if he can renegotiate a more favorable disposition.
I am trying to give you a general answer to your question. We do not have an attorney-client relationship by this response on the avvo website. I have not been retained to represent you. I am licensed to practice law in Kentucky and in federal court in this state and the Southern District of Indiana. You need to seek legal advice from an attorney licensed to practice in your area..
Prior to being able to more fully answer your question, I need to know the following:
Did you request a hearing for the traffic citation? If so, did you do so in the time allowed? If so, did you attend the hearing? If so, did you plea guilty, no contest, or not guilty?
Did you elect to enroll in driving school or were you ordered, by the Court, to do so? Were you adjudicated prior to having enrolled in the driving school?
Did you ever elect to take the driving class in the past? If so, how many times and when?
If you would answer these questions, I will be able to give you a much better idea of why you have points on your license.
The above advice is intended to be educational only. Any legal issue(s) should be brought to the attention of a licensed and qualified attorney in your state of residence. No attorney-client relationship exists or should be construed to exist by virtue of this post.