"I want to attend Chapel" - please provide advice on how I can better my essay.

As I soared through the air upside down, my heart throbbing in my throat, I heard my cue - "Hep!" I released my white-knuckle handhold, threw my arms high above my head, and waited, praying silently, for my savior to catch my wrists. In that split second of dizzying weightlessness, of heart-stopping free-fall, I wondered how I had gotten myself into this awesome situation. Before I could conjure my thoughts together enough to answer, though, my wrists slammed into my catcher's hands. He tossed me safely down to the net and my trembling legs found solace on the wonderfully solid ground.
The trapeze was something that I, like millions of other people in the world, admired, but never imagined myself doing. When my mother came home one night and informed me that a local company had set up a real-life, professional trapeze, I could not resist its lure. The two-hour session would include a beginner-friendly position that would eventually be caught by a professional catcher. It sounded perfectly terrifying, but curiosity pulsed through my veins; soon I found myself staring aghast at a mass of net, wires, and bars that appeared entirely unsafe and unstable.
Swinging on and around bars was nothing new to me – I had participated in gymnastics since age two and felt quite at home hanging on a bar. However, the trapeze added one element of physics to the bar that changed everything I had grown accustomed to – motion. In gymnastics, the bar does not move; rather, the gymnast moves and performs difficult tricks around the stationary bar roughly eight feet above the ground. The trapeze, however, required both the bar and the acrobat to move, and, to maximize the fear factor, was positioned three times higher than a set of gymnastics bars. Simply the sight of the trapeze bar from the ground was enough to set my legs to trembling – how was I going to accomplish anything off the ground?
After brief introductions and basic instructions, the instructors informed me of the rules of the ladder. Once I climbed up the ladder to the platform, I couldn't climb back down – I had to swing. This was my only chance to back out from the activity, but I couldn't stop. I wrapped my fingers firmly around the rungs and stepped carefully onto the ladder, climbing slowly. I couldn't think, my mind was being driven by curiosity; I stepped onto the platform and allowed the instructor to fasten my harness to a rig of bungee cords. My toes hung over the edge of the platform, my sweaty fingers gripped the taped bar; I heard my cue – and hopped from the platform, swinging into motion.
I safely completed the beginner-friendly trapeze course and slept soundly that night, unaware of the addiction that would spawn overnight. I realize now that I want to attend Chapel Hill for the same reason that I went back to the trapeze two more times – curiosity, my thirst to experience, overwhelmed me, and now I crave to experience everything that Carolina has to offer.

I like this piece a lot! It's lively and unique. But it both loses steam and becomes confusing in the final paragraph. What "addiction that would spawn overnight"? Better to leave that out, whatever it is, in favor of filling out what you say about why you want to attend Chapel Hill.

That said, here are a few minor suggestions/corrections:

"Awesome" is technically correct but not quite right due to the associations of the informal use of the word to mean, vaguely, "especially good." Find another word.

The trapeze, however, requires both the bar and the acrobat to move

I couldn't think clearly; my mind was being driven by pure curiosity. I stepped onto the platform and allowed the instructor to fasten my harness to a rig of bungee cords.

"I couldn't think, my mind was being driven by curiosity;" It sounds a bit odd to talk about "my mind", instead of just "I." Also, curiosity isn't usually associated with blocking out thought, and doesn't really work with the physical symptoms you describe. Perhaps you should focus instead on your fear, and how you overcame it, as that is sort of the trajectory the rest of your essay follows.

I released my white-knuckle handhold, threw my arms high above my head, and waited, praying silently, for my savior to catch my wrists.
^^'Praying' is not gramatically parallel with the other tenses in the sentence.

'The two-hour session would include a beginner-friendly position that would eventually be caught by a professional catcher'
^What is caught??

It sounded perfectly terrifying
^ahhhh is that a juxtaposition I see.

'rather, the gymnast moves and performs difficult tricks around the stationary bar roughly eight feet above the ground'
^It is after a semicolon, so you can omit 'rather'.

'The trapeze, however, required both the bar and the acrobat to move, and, to maximize the fear factor, was positioned three times higher than a set of gymnastics bars. '
^Did it require only at that time, or does it still require?

Simply the sight of the trapeze bar from the ground was enough to set my legs to trembling – how was I going to accomplish anything off the ground?'
^my legs to tremble?'

'I heard my cue – and hopped from the platform, swinging into motion.'
^and swung

'curiosity, my thirst to experience, overwhelmed me, and now I crave to experience everything that Carolina has to offer.'
^my thirst for experience overwhelmed me ( You do not need a comma after 'experience'

and now I crave to experience everything that Carolina has to offer.
^You can remove 'and', and allow it to become a new sentence.
Furthermore, do you want to experience everything that Chapel Hill has to offer, or what the state of Carolina has to offer?

*This is a good piece. However, you can perhaps develop the reasons to attending Chapel Hill a bit more. You narrated everything quite well, and suddenly you link it to Chapel Hill and then end it in a matter of a sentence.

Interesting read. Try to cut down on the double statements, 'unsafe and unstable' . They're unnecessary, and they slow down the pace. So do adverbs like 'wonderfully'.