What can i do if I have been falsely accused of ual harment at work?

I recently had to deal with being falsely accused of ual harment in the work place. An investigation was completed after about 1 month and the decision was made which determined the accusations were indeed false and unfounded. My employer continued to have me work in the same department with my accuser as if nothing had happened. Is there some sort of rights or recourse that I have in being falsely accused? Should these people not be subjected to the same punishment for a false allegation as I would be if they had been true? I would have lost my job. Isn't my employer responsible for now creating a hostile work environment for which I am now completely uncomfortable? This is driving me insane. I get falsely accused , it is determined by my employer that the allegations were false, but now I have to continue working with these people because they were not punished. This is a medical environment. This, in my opinion is an integrity issue, a defamation of character, and creation of a hostile work environment. Please help with any advice possible.