You may have an action to recover under 42 USC Sec. 1983 against the individual that swore out the false affidavit, and/or the arresting agency, but it will require that you hire an attorney to review the facts of the case, and the reasons that the court of appeals overturned the conviction, and the specifics of the dismissal action below. There is a line of cases (Heck v. Humphries, and its progeny) which generally prohibit 1983 actions for those convicted of a crime, where any factual or legal issue might have the effect of contradicting the criminal conviction. You should have an attorney who handles civil rights cases review your matter.
The opinions expressed in this answer are meant for educational and public service purposes. Requesting general information about the law on a public website should never be a substitute for a personal consultation with an attorney who can give specific legal advice tailored to the facts of an individual case. Please be aware that Robert Hogan is licensed only in Texas and New Mexico, and that any opinions given are not meant to apply outside of these states. No attorney-client relationship is intended by answering questions or emails.