Texas has limited whistleblower protection. Texas Government Code Sec. 554 protects public employees who report violations of law to the appropriate law enforcement agency. See statute. The Texas Whistleblower Act provides for a 90 days deadline in which to file suit. It also requires an employee to first file a grievance if the state or local agency provides for a grievance procedure. If the employee files a grievance, then the duration of the grievance will toll the statute of limitations (ie, toll the deadline).
The good faith report of the violation of law would need to be made to the appropriate law enforcement agency. Note that provision means simply reporting to a supervisor at work will not suffice.
There is no equivalent statute for private employees. There is no whistleblower type protection for private sector employees. But, as I wrote earlier, a private employee would be protected if s/he were required to violate a criminal statute. See my prior post.
So, if you are a private employee, if you report your employer for violating some criminal law and get fired, then you have no protection. If you are a state or local government employee and are fired because you reported your employer for violating some law, then you may have the right to file a lawsuit. See a qualified Texas lawyer to discuss any such lawsuit.