You need to call an employment attorney in your locale who can advise you specifically what your rights are. In Texas it woulds be unusual to not advise an employee who was making the allegations against you. Of course, Texas is a hire and fire "at will" state. Go see an employment lawyer.
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I agree with my colleague that you should speak to a lawyer ASAP to evaluate your options. If the "right to work" (right to be fired for almost any reason) aspect of state law allows you to be terminated, you may not be able to learn the identity of your accuser unless/until you sue for wrongful termination.
I have been licensed to practice in the State of Oregon since 1990. I am not offering legal advice regarding your question, only general information regarding the law. You are not my client nor am I your attorney unless we sign a retainer agreement.