Your question contains somewhat contradictory information. If you were not arrested, how can you owe a fine to the Court. Generally a person charged with shoplifting has two charges. Larceny and Criminal Possession of Stolen Property. If the property stolen is worth less than $1000 the charges would be misdemeanors. Misdemeanors in New York are crimes and a conviction for any misdemeanor would leave you with a permanent criminal record. This is not a matter to be taken lightly. Please contact a lawyer. Since Petite Larceny is a crime involving moral turpitude it can affect your citizenship application.
Sometimes stores will not call the police but will detain you if you are caught shoplifting. Sometimes they will have you sign something that says you must stay out of their store and if you are caught you will be charged with trespassing. If the police were no involved, then you were not arrested. If there was no arrest, there is no criminal record.
It sounds like you may have been given a desk appearance ticket. It will only show on your record if you were convicted. In the Bronx, first time petit larceny charges tend to get reduced. A single petit larceny is not usually a problem with immigration