Can I write a letter to the prosecutor and the judge explaining my side of the story?

NO! it is not advisable for a Defendant in a Criminal Case to say anything to the Judge or to the District Attorney because anything a Defendant says to anyone, other than to their own attorney, either orally or in writing, can be used against them!

Further, it is against the New York State Administrative Rules of the Unified Court System, for a Judge to accept or consider communications made outside the presence of all the parties to a pending proceeding.  Therefore, any attempt to contact the Judge in such a manner will likely only result in the letter being sent back and copies of it being sent by the Court to everyone involved in the Case. 

The Defendant’s Attorney is charged with the duty to serve as their counselor and advocate, and to render effective quality representation.  In accordance with this duty, a Defense Attorney is in the best position to communicate with the Court and the Prosecutor and to so advise the Defendant if s/he desires to be heard.