wrongly accused of cherry picking

A false accusation is just a factually incorrect claim of wrongdoing. There's no fallacy by default.

If accusations are used in the context of a wider argument to distract from some weakness in the speaker's case - especially if the accusations are baseless - they could fall under some fallacy category. To be broad, these would all be considered relevance fallacies.

One example could be ad hominem (tu quoque) where someone accuses you of hypocrisy, and uses your supposed hypocrisy to suggest your conclusion is false. This cannot be the case - the truth of the conclusion is independent of the person making that conclusion - and is a fallacious tactic, more so when the accusation is baseless or even false.

There is no false accusation fallacy. Every (informal) fallacy is an argument itself. If someone has accused you of a fallacy, and you disagree, then make your case as to why it is not a fallacy. I never heard of "reverse cherry picking," but I guess you can add "reverse" in front of most fallacies and call it a new fallacy.

Tip: When defending oneself against an accusation of a fallacy, it is best to define the fallacy first so your opponent knows that you know what you are being accused of, then explain why it is not that fallacy.