Since you also have your own side of story, you may file a cross FIR against her narrating your side. If the SHO of the concerned Police Station is reluctant in lodging the FIR then you may File a complaint u/s 190 CrPC before the Magistrate of your area.
Apart from defending the FIR which had been lodged against you, the filing of counter FIR will give you some settlement leverage. Further, it is unlikely that the police will record your side of witnesses in the FIR which was lodged against you.
But you will have to move quickly with filing of a counter FIR since this delay will weaken your case. If you are not able to register a counter FIR, then try and persuade the police to add your side of witnesses in the investigation.