What sort of legal action can I take against her for doing this to me?

I don't want to diminish your situation, but what do you hope to gain by taking legal action?

In general, the legal system has criminal and civil components, the former sees the state prosecute and punish people for breaking the law, the latter sees people paid money to be "made whole" after suffering a financial loss (such as violating ordinances about the return of rental security deposits).

You could go to the police and ask them to prosecute her. They likely won't because if they were inclined to they would have probably done so already.

You could also take her to civil court and sue her there. It's been tried but just because someone can file a lawsuit doesn't mean they will win that lawsuit. You'd have to prove she lied and you'd have to show financial damages as a direct result of that lie. From your narrative, it seems unlikely that you could prove a negative (that you didn't rape her) just as the DA couldn't prove the positive (that you did rape her). And furthermore, you'd have to ask yourself two questions. The first is whether or not pursuing a lawsuit would be in your best interest, psychologically. Could this make things worse for you psychologically? Would such a lawsuit hamper your ability to get beyond this and heal? The second question is: even if you somehow won, even if she admitted she lied, would she even have money to pay you? And if she did, would that money fix you?

Taking everything you've written at face value, believing it all 100%, my non-legal advice is that taking legal action her probably isn't going to be what helps you move past this. You're already taking steps to heal. Talk to your new psychiatrist and see what he or she says. And if you still are tempted to take some sort of legal action, speak to a local civil attorney about what that would take. Good luck.