Right to work means that they cannot force you to join a union. Wrongful termination actions in Florida are very limited. However, if you and your co-worker were treated differently you may be eligible for unemployment benefits, unless you have a previous history and he does not. You may want to consult with an employment lawyer on those issues, and see if there are any other facts that might give you some cause of action.
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If your coworker clocked you in and you did not self-report it to your employer, you likely will not have a wrongful termination claim as the termination was clearly for a legitimate business reason. However, if your coworker is not in the same class as you (ie. race, gender, disability etc), then you MAY have a case. Best of luck!
This is general information only and does not constitute legal advice, nor does this communication in any way establish an attorney-client relationship. Feel free to contact me directly for further information at 239-985-9691.