You could have a case of false imprisonment, you should go see a local personal injury attorney who can better advise you of your rights. At a store like Costco they probably have pretty good surveillance footage which maybe strengthen your case if it shows security acting unreasonably. Get to an attorney ASAP so they can make sure that Costco preserves rather than destroys the footage.
The LP could not have given false testimony if he didn't show up to court. Testimony is statements under oath. I think you meant to say that he made a false report to the cops.
But is the LP guy the person who caused your injuries -- or was that the arresting officers?
The fact that you were arrested while under the influence of medication can cut for you or against you, depending on some details not available here.
You need a private consultation with a personal injury attorney.
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