Hello and thank you for entrusting me to assist you. My name is ***** ***** I will do everything I can to answer your question.
I am very sorry to hear that this happened. In general, though, I must tell you that employment in the state of Texas is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
Thus, an employee can be terminated on the basis of false allegations of sexual harassment. Since the employer doesn't need to justify their reason or have a true or correct reason, the law does not entitle an employee to an investigation or opportunity to defend themselves. Again, since employment is at will, either the employer or the employee can terminate the employment relationship at any time.
So, regrettably, your only option would be to attempt to reason with your employer. It is not in their interest to terminate an employee for no reason, so they should be reasonable in working with you. Again, though, they don't have to be, and your only power is the power of persuasion.
I hope that you find this information helpful and am genuinely sorry if it is not what you were hoping to hear. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.