Even though everyone calls the law the "texting while driving law" it actually prohibits more than that. This is the Laredo law on cell phone use while driving:
Sec. 19-224. - Regulating the use of hand-held mobile communication devices while driving.
In this section:
Hand-held mobile communication device means a text-messaging device or other electronic, two-way communication device that is designed to receive and transmit voice communication, text or pictorial communication, or both, whether by internet or other electronic means. The term includes a mobile telephone, and a personal digital assistant (PDA).
Text message means a two-way communication (whether real-time or asynchronous) in which data (composed in whole or in part of text, numbers, images, or symbols) is sent, entered, or received by a method other than by voice and transmitted through either a short message service (SMS) or a computer network.
Wireless telephone service means two-way, real-time voice telecommunications service that is interconnected to a public switched telephone network and is commonly referred to as cellular service or personal communication service.
A person commits an offense if the person uses a hand-held mobile communication device to send, read, or write a text message, view pictures or written text, whether transmitted by internet or other electronic means, engage in gaming or any other use of the device, besides dialing telephone numbers or talking to another person, while operating a moving motor vehicle. This section shall not apply to public safety personnel in the normal course and scope of performing their duties.
It is an affirmative defense to prosecution of an offense under this section if a hand-held mobile communication device is used:
While the vehicle is stopped, out of the moving lanes of the roadway;
Strictly to engage in a telephone conversation, including dialing or deactivating the call;
As a global positioning or navigation system that is affixed to the vehicle;
To communicate with an emergency response operator, a fire department, a law enforcement agency, a hospital, a physician's office, or a health clinic regarding a medical or other emergency situation to prevent injury to a person or property;
In the reasonable belief that a person's life or safety is in immediate danger; or
Solely in a voice-activated or other hands-free mode.
As you can see in the underlined portion, the law also prohibits the reading of text or viewing of pictures on the phone while driving as well, not just texting. So you will have a hard time challenging the ticket just on the basis that you were not texting because just reading things on your phone while operating a vehicle is also prohibited by the same law. The only defense that might be available to you would be that you were stopped, but that requires that you be out of the moving lanes of the roadway and it sounds like you were in the street due to the line, so that defense would also be hard to invoke. Sorry I can't give you better news.