A Customer Claimed That I Gave Her An Empty Envelope Without Money Leading To A Serious Investigation

Hello, I'm here for legal advice.

I work for a big named Bank as a teller in the state of Texas. My job is to help people with their daily monetary activities. One Saturday, I helped this lady withdrawal about $3500 from her account. I had counted the money in front of her, put the money in a white envelope, handed her thr envelope with the money inside, and that was the end of our transaction. She then came back into the bank 4 days later claiming I gave her an empty envelope insinuating that I stole the $3500 from her. I was not there that day so my coworker filed a complained on her behalf leading the security company that is contracted to our bank to begin a serious investigation on me, all my previous transactions, and my financial situation.

I know most people will say if you follow policy, then you have nothing to worry about since you have the camera watching your back. Now the probably will this is that this is not my first time being accused of stealing money from customer. The last time it happened, I also thought the camera will capture everything and it eill prove that I am innocent. Wrong! They did pull an investigation on me at that time and they told me "the camera was not working for the last 2 months" afterward they then said "the camera was working but the angle did not capture you counting and handing the money to the customer." Lucky at that time that customer came back to report that she found the money. Ever since then I'm too afraid to trust my bank to have my back again.

So my question is Lawyer of Reddit, do I have a case for defamatory of character on my hand? I know in the state of Texas to be able to sue for defamatory of character, I must be able to prove the following elements; False Statement, Defamatory Statement, Publication, Faults, and Demages.

1. False Statment: the customer claim that I gave her an empty envelope insinuating that I did not give her the cash she withdrew
2. Defamatory Statment: same as above
3. Publication: She made this statement at my workplace to my coworker which who then by company policy had to make a complaint which is now on my record
4. Faults: I withdrew the money for her on a Saturday, it took her over 4 days to come back to claim that I gave her an empty envelope. She than claimed that she did not know if the envelope I gave her had the cash in it or not, insinuating that I could have given the cash (which I know for a fact 100% that I gave her the $3500) but she lost it or dropped it. This is negligent on her part.
5. Demages: This has greatly caused me emotional demages as well as demages to my professional reputation as there will now be a serious investigation that follows this claim she made. Also I am at risk for termination as well.

With all that being say, do I have a chance at suing her for defamatory of character?

Another question, I do move forward with this lawsuit, can I legally request that my bank turn over the security footage as prove of my innocent? The reason I ask this question now is because my bank's security company does not allow employee access to these footages. Can I get a legal order for the bank to turn over the footages?

Follow up question, if I were move on with this lawsuit, what are the chances I will win?

Thank you for your time and hard works. Please help your girl out. I am so tired of this bullshit. Honestly.