If your actions constitute a crime involving moral turpitude, you will have a problem. Best to contact immigration attorney who does criminal work.
I agree that consulting with a lawyer experienced in the specialized area of immigration law would be wise. My suspicion from what you have said is that you have not yet been, and likely will not be, charge with Retail Theft or shoplifting. IF you already have been charged criminally or receive documents from a court demonstrating such event, then you should immediately be in contact with legal counsel if that had not already been done. Good luck. Btw, you can ignore the letters demanding that you pay a civil demand.
Given what you have said you were not charged criminally. However, the fine they mentioned is not a fine they were probably referring to a civil demand letter. You will most likely get a letter demanding a amount of up to $500. I would just ignore the demand letter, the stores rarely follow through with trying to collect via civil suit. However, if you receive a summons to appear in court see a criminal attorney immediately.
David Newton, Esq.
This is not intended as legal advice and does not create an attorney-client relationship.