I like the topic of your essay, and you're a very eloquent writer, but you kind of glossed over the "challenging-ness" of your challenge through the second paragraph. For example, you could take out the worrying the night before and skip to the first time you smiled at the stranger as you walked into school. You could spend more time describing your nervousness and frustration with always being shy. Emphasize that even though you face the same shyness every time, THAT was the time when your determination was greater than your fear.
Also, the lessons you learned from your experience are true but also cliched. Talk about why it was so important to you to overcome your shyness and why it's so important to keep confronting your fears.
Some small grammar things, depending on what you want to keep:
The night before my first day of high school, I lay awake in my bed wondering how I would make new friends, how I would talk to people, what if the teacher asks me to read out loud in front of the class.(This might look better formatted like dialogue: I lay awake in my bed. How will I make new friends? How will I talk to people? What if the teacher asks me to read out loud in front of the class?)
That night, that I decided to make a change.
I would do one thing every day
My shyness didn't define me anymore; I was no longer 'the quiet one'
Shyness may seem like an effortless hurdle to overcome, but for me it was a learning process. It wasn't something that could be accomplished in a day; in fact, it took years. This journey helped me realize that nothing in life can be accomplished with a snap of fingers; one must work to reach his or her goals. (This last sentence sounds a little awkward.)
Good luck!