TX state law says that you must have a conviction or indictment for a felony, Class "A" misdemeanor, or Class "B" misdemeanor to become ineligible for a CHL. (There are other limitations, such as having been committed to a mental institution, but they don't directly relate to this question.) Since you paid the fine, you should be OK. Minor traffic violations aren't serious enough to make you ineligible.
Even if there was a bureaucratic snafu regarding the fine, nonpayment of red light camera fines in TX is legally
not the same as nonpayment of other traffic tickets. Believe it or not, a red-light fine is
not a criminal traffic violation; it's a
civil penalty that's levied against the vehicle owner. If it were a criminal penalty against the driver, the normal rules regarding due process and burden of proof would kick in, and the municipality would have to prove the identity of the driver beyond a reasonable doubt, which is nearly impossible in most red-light camera cases. The state sidestepped this problem by making it a civil penalty.
Since the penalty is civil and not criminal, enforcement of nonpayment must be done through the
civil court system rather than the criminal courts. AFAIK the municipality cannot directly issue an arrest warrant or indictment for nonpayment of TX red-light fines. The municipality would
first have to pursue
civil court action, then you would have to fail to appear in court or otherwise violate the rules of civil court procedure before a warrant could be issued.
Yes, it's screwy, but I didn't write the law.
Mandatory disclaimer: I am not an attorney, nor do I play one on TV. This is not official legal advice. Caveat emptor.