Couldn't you take a defensive driving class and have the ticket dismissed? In Texas, the cost to do this is about the same as the ticket, but it doesn't go on your record.

Another trick that is used in Texas is to request 'Deferred Adjudication" from a judge. This is similar to probation; you pay the same fine but if you are not convicted of another offense within a certain time period (say 12 months) the conviction does occur and your driving record remains clean.

Since you seem to admit that you committed the offense, unless you have a philisophical reason to fight the ticket, you should be looking for the cheapest solution. You might want to talk to a lawyer about your options at this point. It sounds like you are doing this alone without much knowledge of the law. This is almost certainly a mistake.