If there are no damages, there's no grounds for suit.No actual "damages" yet to report, only the humiliation of going through such an investigation and emotional stress of the past week.
Even if there WERE grounds for suit, are you certain you could afford to bring forth an action? And if you prevailed, do you think you'd actually be able to collect the damages?
Cooperate with HR. Don't be stubborn, don't withold information. If you're asked a question, answer it honestly. Failure to do so could cost you your job, and you wouldn't have grounds for a wrongful termination suit, either.

