You cannot drop the charges against your ex, but the DA will probably need your cooperation in order to convict him. Unless your ex has foolishly admitted to having sex with you or someone else can prove that you've had sex, then it is only your in court statements against him that can be used to prove the case. If you do not want to cooperate with the prosecution of your ex, then don't make any statements to anyone about the case and wait to see if you are subpoenaed to testify. If you are subpoenaed, you have a right to a free attorney and you can discuss with that attorney any potential legal reasons you may have for not having to testify. Good luck.
Only the DA can make the ultimate decision. But the DA will have a weak/difficult case if you are not willing to cooperate. I would contact the DA and see if you can talk to that office. Once charges are filed though, and the ball is rolling it will get harder, so you may want to act fast.
San Diego Criminal Defense Attorney
Mr. Pullman's answer is correct. You cannot drop the charges. That is a TV fantasy. Cases are prosecuted in the name of the People of the State of California because the law deems crimes committed against the state, not an individual.
If there was no sex or violation of the law, there is no case, and you have the right to tell the DA or anyone that. You don't have a right to lie about it, and should not lie about it. Also, you have no obligation to speak with your parents, a cop, the D.A. or anyone about any of this. If you receive a subpoena to appear in court, that may be a different situation. You'll need a good lawyer to handle that part.
People don't drop charges, DA's drop charges.
If you, the minor emancipates yourself through the courts, your parents will have less ability to meddle (and less duty to support you-choose your allies and live with the decision).