I love the story, and the essay has really good flow and varied sentence structure. I'd use a little more description though. You tend to use simple words like "people" and "school" over and over when you can replace them with words like "crowd" or "campus" or "building" or whatever is appropriate in the context. Like in these sentences:
I stepped out of the car and walked proudly through the front gates of the school . I had only known a few people from my old school who were attending the same high school as I was, so I had to get to know new people.
You can change school to campus or grounds or something along those lines, and you use the word people twice in one sentence which is kind of redundant. Rephrase it like "I only knew a few kids who were going to this high school, so I had to try and make new friends." You also use the words "braces" and "teeth" a lot. And yes, I know it's what your essay is about but if they've really changed who you are then I think they deserve some more attention. Use similes and metaphors and compare them to things like train tracks or zippers that would keep you from smiling idk...and for teeth you can say "pearly whites" or describe just how crooked they are (are they twisted? missing? spaced out? crowded?) to give a visual. They are your focus so you need to highlight them.
One last thing is in the first paragraph I get really confused because you talk about how you proudly smile, but you're nervous, and then you're confident again, and then you're uncomfortable. Pick one. Either you feel good walking into school or you don't, or you do until you introduce yourself with a smile and people see your teeth but you can't go in between like 5 emotions in 2 sentences.
Other than word choice and the confusion in the first paragraph I think it's really good! And its a super interesting and unique topic! Good luck!