Your choices are to either pay the ticket, with Texas MV then informing the NY MV agency about the conviction; or, you can hire a Texas lawyer to represent you in absentia to try to negotiate a better disposition. (Which will still be reported to your home State MV). If you want to take the case to trial, either with or without a lawyer, you will most likely end up re-visting Texas to attend the trial. Good luck.
DISCLAIMER I do not practice law in your State. This answer is provided solely for informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.