Take everything you write and put it in a drawer somewhere. Make a binder. Have a folder on your computer (and back it up!). Whatever system you come up with, make sure you have a secure place to keep your writing. Even if you think your work sucks. Even if you know it sucks. Save it.
Why? Because it's yours. Because your life is finite and so are your memories. One day you will wonder about that story that you wrote when you were thirteen. You will try and try to remember it but you will only be able to recall the edges of it, the feeling of it, and maybe not even that. Maybe you won't remember it at all. And chances are, that story you wrote when you were thirteen probably won't be any good. If you did save it, you'll always be able to go back and cringe at your shallow characters and silly dialogue. But it's more than that. That story is a piece of you. It has you-from-the-past stamped on each and every word. Reading it won't turn back time, but it'll be close. In fact it's as close as your future self will ever be to being thirteen again.
One of the first writing books I ever owned was Writing Magic by Gail Carson Levine. She talks briefly about this in the first chapter and I think she puts it eloquently:
"When you become a teenager, you step onto a bridge. You may already be on it. The opposite shore is adulthood. Childhood lies behind. The bridge is made of wood. As you cross, it burns behind you."
She goes on to say that if you keep your writing...
"You'll be able to see yourself in that lost country. You'll be able to wave to yourself across that wide river."
Obviously the moral of this story is to keep the writing you do as a young person, but what if you've already lost a lot of what you've written? Don't worry. Instead of dwelling on the past, look to the future. Start saving everything you write, even those seemingly meaningless paragraphs you compulsively delete. Save it, make a new document, and keep writing. You'll be so glad you did.