If you are cleared of the charges, you can attempt a suit against the store. The question would be what amount of damages would be appropriate based on the three or four hours you spent in a precinct waiting for your DAT. It might be worth exploring the issue with a civil attorney if you are successful in the criminal matter. Good luck.
This answer is only for informational purposes and is not meant as legal advice.
You should focus on the criminal case first. Your "admission" undermines a civil lawsuit as does a statute that gives stores immunity in cases like this if they have a reasonable basis to think you are stealing.
The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.
First fight the charge, win and then consider a lawsuit.
Please do NOT use this answer/response to say or do anything regarding your situation. This answer/response is based on the information provided in the question asked and requires a much more complete context than is available in this public forum. BEFORE you say or do anything consult with an experienced Federal and/or state criminal defense attorney in your jurisdiction who will listen to you and your concerns.
Even if you were to get the criminal charges dismissed, I'm not sure you will find any attorney to bring a wrongful arrest suit where you admitted to the security officer that you did what they accused you of. The admission alone is not likely enough to convict you in the criminal case but you may want to to rethink a strategy that admits to a crime because you're in a hurry. I would hire a criminal attorney to represent you so things do not get worse. If you are convicted of a crime in New York, there is no mechanism to have that record expunged at a later date.
I am a former Brooklyn Criminal Court Deputy Bureau Chief with over 17 years experience specializing in handling criminal cases. All answers are for information purposes only. Answering this question or any future questions does not form any attorney-client relationship. Be mindful, that answers are limited by the limited facts presented by the questioner and are not meant to take the place of competent legal advice by an attorney fully informed of all the facts surrounding your case. Also, be aware that nothing posted in a public forum such as this can be deemed confidential or privileged communication.
The police always advise you of your right to remain silent for a reason. Never admit to anything that you HAVE NOT DONE.
Concentrate on the outcome of the criminal matter. With the outcome of the criminal matter in your favor, ask your criminal attorney if he or she is familiar with another attorney who handles wrongful imprisonment cases. Most criminal attorneys know of someone that could help.
This does not constitute legal advice or the engagement of my services as an attorney.
I handle both criminal defense and wrongful arrest cases. As my colleagues have stated, because you stated to security that you switched the tags, because you were detained for a short period of time, because you didn't have property wrongfully seized from you for an extended period of time, because you did not lose your job over this incident, etc you likely do not have a claim to sue Century 21.
That being said, you will want to minimize the effects of the DAT. I've handled these types of cases (where someone is wrongfully accused of shoplifting) in the past and had excellent outcomes. Since you confessed (regardless of the veracity of the confession), I recommend getting an attorney who can fight the underlying assumption of guilt.
Good luck with the criminal case.