Nominal damages will be awarded to an individual who has suffered no actual damages in consequence to the illegal confinement. In cases where an injured offers proof of injuries suffered, s/he will be compensated with damages for physical injuries, mental suffering, and loss of earnings.
If you are referring to the tort of false imprisonment, then the answer is yes. You can file a civil lawsuit against someone or an entity that falsely imprisoned you. However, outside of an extreme situation, the problem is that there are rarely any actual damages. Therefore, a lawsuit is rarely worth doing.
Generally speaking, false imprisonment, including false arrest, has two elements: an intentional restriction of a person's freedom of movement without legal right; and. the intentional use of force, words, or acts which the person restrained is afraid to ignore, or to which he reasonably believes he must submit.
If the false accusation harmed your reputation, you can file a defamation case: Civil Defamation: Claim damages (monetary compensation) under tort law for the harm caused to your reputation.
False Imprisonment Defenses. Consent, justification, and self-defense or defense of others are all defenses to hostage false imprisonment.