I actually enjoy reading this piece. I don't know about the admission but for me, I think you did show your personality through your writings even though you did not directly stated it.
I just have some little suggestion, because some of your sentences are "telling," but by taking off some unnecessary words, they can be great "showing".
Numerous books and binders are sprawl across my bed, reminding (use another word that indicate foreshadowing such as forewarn or something along those line) me thatI will undoubtedly be awake until midnight or later another sleepless night trying to memorize a soliloquy by Hamlet and editing pages from the latest yearbook deadline.
My pre-calculus book feels heavy in my lap but it barely weighs anything in my mind.
I like this line :)
I slide push the book and its impossible plethora of equations to the side as I look out the nearest window and sigh.
Outside, I notice that a willow tree is crying in the wind as the sun sends sparkles of hope over the sad foliage.
longed for.and my stomach turns (twists)
A train chugs by parallel to my car, and I hearits staunch whistle in my ears
"Where are you heading to? Don't you want to know where I'm going?" but they never hear me because they are going, going, gone. (something wrong with this part, try to see if you can fix it)
Your conclusion you kinda lost the tone that you had. Try to rephrase the who part to see if you can make the transition smoother.
That's all I have and feel free to select whatever you think is useful since this is only one person comment. Good luck getting into your top choices. Happy holiday!