Yes,I have witnesses,and I got humiliated in public!
No you can only sue it you got hurt are something
If someone other than the police accused you and told others you stole then you can sue them for defamation of character in civil court
You would have to prove that the person or persons who accused you told others people and that their telling other people injured your reputation. Finally, YOU have to prove that the stories that were told were not true. It is not enough to say that the accuser has no proof or that you did not do it. You have to prove the the stories were not true. Can you do that?