There is first time for every thing, right! So, no worries, if you drive a vehicle, you will get ticket at one point or another.

There are simply 3 options:
Fight the ticket by going to the court
Admit Guilt - Pay the fine. The incident remains on your driving record for certain time.
Admit Guilt - Agree to driving probation and take safe driving classes (like Defensive Driving) - the incident does not appear on your driving record and you pay lesser fine. But you will have to pay additional court costs (in TX it is about $100 for traffic violation cases)

Simple mistakes on the ticket issuing officer's part such as wrong spelling name on the ticket or improper car identification (i.e. calling a red car, 'maroon care' etc.) or inaccurate location where you got the ticket (i.e. wrong spelling name of the street etc.) will automatically get the ticket dispensed - if you fight the ticker and appear in court.

However, you've stated you live in Texas. You might very likely have to appear at a court in NY to fight the ticket (i say 'might very likely' because I am not sure if NY requires people fighting traffic tickets to appear in courts; in TX it is required. So, research NY laws on this). If NY requires defendants of traffic tickets to appear in court to fight the ticket OR to admit guilt and opt for safe driving classes, it might prove to be difficult for you - living outside of NY. Paying the ticket might remain the only option. But do check with them, and see what options you have in cases like yours - there must be some provisions in place. Good Luck.