Hey there, That was a very unwise thing to do, but i guess you did not mean for this to happen. It just shows that things can spiral out of control.
She is trying to speak to you, right? Perhaps you should explain to her what you did, thats if she will believe you. I think the best thing would be to just make up an excuse of why you cant speak to her anymore, otherwise she will attempt to carry on talking to you unless you tell her otherwise. I suppose you two could carry on talking as long as you two are more discreet, but i really would not recommend that.
I suppose you could try and explain the situation. I can more than understand why her parents were so upset and angry because if that was your daughter would you be scared for the welfare of your daughter? For all they knew you could have in fact been 21 like you originally said. If you can explain to the parents what you did and why you did it.
The best thing would be do just move on and forget about her. I know it will be hard, because as you said she was a great person, but you don't want to get reported to the police. Her parents are probably really unsure of you and rightly so, even if you explained to them they would still probably not believe you. They are going to monitor her more stringently. I think you should just move on. Now you know not to make a mistake like that again.
Good luck!