I'm sorry to hear about your unfortunate incident. Unfortunately, however, as embarrassing and as humiliating as an experience as this was for you, it does not rise to the level of something for which you can sue. Not every event that distresses us can be rectified in a court of law.
I am sure that you believe that your character was defamed. On one level, that's quite true. But, what happened to you does not make out all of the elements of defamation of character needed to have a viable law suit. That is to say, you suffered no economic losses or physical injury as a direct result of the incident.
You can write a strong letter to Walmart's manager and to their corporate headquarters, detailing your unfortunate incident and complaining about the inappropriate overzealousness of the store personnel who handled this. You can demand an apology and that these people's position be terminated. But beyond that, you do not have a successful suit.
That said, this does rise to the level of a civil rights case if you cah demonstrate that you were targeted because you were profiled and discriminated against due to your race, religion, age, gender or disability. This is not in your fact pattern, but if it exists you indeed would have a cause of action against Walmart.