Regretfully, federal courts don't require police to fairly investigate all the facts before arresting. The question is "probable cause," and a lie from a witness is just that.
You don't really have much of a case for false arrest. The police officers were operating under the assumption that you were the aggressor. Now that may be false but the cops didn't know that.
I am more concerned with the fact that you might get charged with a crime. If you do please contact an attorney to help you.
The above information does not establish an attorney client relationship nor is it meant to provide legal advice.