If someone accuses me of harrasement at school untruthfully and without proof, what are my rights?

Legally, if someone accuses you of "harassment" unless they go to court and get a restraining order or a temporary restraining order (TRO) there is nothing they can do. But in order to get an order from the court, person must declare "under penalty of perjury" all of the elements of "harassment" in order to get the order. Of course, you have a right to deny the charges after the TRO is issued and the court will set a date for you to appear.

 You have other rights such as a lawsuit for libel or slander.  If the untruthful allegations are written it is libel, but if the person is only making the accusation verbally, it is slander. 

But since you're in California there should be no filing fee for requesting a restraining order to stop the person from scandalizing your good name.