I understand your question, but you are getting ahead of me.
The document you signed does not sound like an employment contract, rather it sounds like you were signing off on the company polices. Florida is an "at will" employment state. That means that an employer may take any action it sees fit in terminating or limiting your employment, unless you have a written agreement with the employer that limits that discretion.
In your case, even though you were falselly accused, the employer has every right to take these suspension actions. In Florida, as in many other states, the employer can fire you for absolutely no reason whatsoever. So, in short, you don't have a legal claim against the employer unless you have an agreement that says they will not terminate you or suspend you unless they have just cause. If you have this agreement, then you can make a claim. However, if there is no written document that is a binding contract which states that the employer can only suspend you for just cause, then you don't have a claim.
That being said, you could sue the patient for defamation, fraud and interference with business relations.
Sorry to be the bearer of bad news, don't shoot the messenger.
Please rate my answer positively so I can receive credit for my work.
Also, if you want to talk through this issue more or you want to see law, or anything like that, just let me know and I'll be glad to walk it through with you. Also, if you think that there is a written policy about just cause suspension with your employer, then try to find it and write me back and we can talk more about it.