As I covered in this post here, New York State does recognize common law marriages from other states.
So long as the common law marriage was valid, to get the marriage annulled, you must show the marriage is void or voidable. A marriage is void if it is incestuous or bigamous. A marriage is voidable for lack of legal age, incapacity to give consent for want of understanding, physical cause, mental illness or where the consent was obtain by force, duress or fraud.
In order to obtain an annulment, you must establish facts that demonstrate the marriage was void or voidable.
Based on the facts you have described, it is difficult to tell whether you have a sufficient factual basis to justify an annulment. For legal assistance contact a New York Attorney