Why is everyone going on an on about how this isn't supposed to be a creative writing piece? What's wrong with creative? Yale asked for 250 words on whatever you want. They didn't say "write 250 words on a topic of your choice, as long as it's not a creative writing piece."
I thought the essay was great. If there's anything I would add, is maybe a sentence or two more about how you grew, instead of the incredibly vague generalities of "I became stronger, yadda, yadda, yadda" Not too much, but just something to focus in on a bit. But otherwise, fantastic job with the 250 words. It's revealing, and gripping, in that there's a lot of information not explicitly provided. And I don't think you have to reveal who "she" is. If you choose to, that's fine, but I feel that it works without that info.