If you cannot afford an attorney to sue her, and cannot convince one to take it on contingency (likely because she lacks the money to pay off any award), then you may be out of luck. If neither the police nor the prosecutor are willing to pursue her for making false reports, then it is likely because they cannot prove definitively that the allegations were intentional falsehoods.

About all you might hope to do at this point is avoid any and all contact with her. Period. None. Zero. Zip.