Contact a local attorney through the bar association or an internet search and see if he/she can appear for you to clear them up for you.
I am a criminal defense attorney practicing in Nassau, Suffolk and New York City. The above information is not a substitution for a meeting whereas all potential legal issues can be discussed.
The key to resolving your problem is knowing what the result was. Generally, speaking, if the cases resulted in dismissals or acquittals, they can be "expunged." If they resulted in deferred adjudications that were successfully completed, they may be eligible for "Orders of Nondisclosure." If they resulted on probations or other forms of final conviction, they will remain on your record unless they are somehow overturned or pardoned.