New York doesn’t expunge records. Disorderly conduct is not a crime and you don’t have a criminal conviction on your record. This shouldn’t be an impediment to your getting into the navy but I would suggest that you check with your recruitment officer.
At worse, the Navy will wait until your conditional discharge has expired. IF the CD is still pending the Navy will usually not accept you and you sometimes have to go back to court to get it changed to an unconditional discharge (a UD). Conditional discharges expire within one year of the date of your sentence. Good Luck!