Dear Linda,
I'm glad to hear that you would like to visit China.
At the beginning, I'm sorry that your parents do not allow you to come alone.
However when I try to think in their shoes, I can understand their concerns.
Every Mon and Dad will worry about their child, especially in their young ages.
Maybe you can try to persuade them with your points.
On the one hand, tell them the meaning of travel alone to a teenage like you and me.
Like it is a symbol of grown-up and independent.
On the other hand, tell them what will you prepare for this fantastic trip.
What is your itinerary, what is your destination and so on.
Even if they will not allow you to do so now, they will let you go sooner or later.
By the way, I am looking forward to show you around in China.
Your sincerely,
Li Hua