"Invent first, and then embellish!"
So advised Samuel Johnson, the eighteenth-century English curmudgeon, wit, and writer.
Now don't think for a minute that Dr. Johnson was advising writers like you to make things up. He wasn't. He was recommending that writers, be they a young minister who had sought his advice on writing a sermon or you confronting the need to write personal statements and application essays, first create a draft that you can work with and then edit it for coherence, logic, writing mechanics, clarity and all the qualities that contribute to good writing. Don't edit as you write that first draft.
Dr. Johnson's works are still being read almost 300 years after his death. I doubt if your personal statement requires that kind of longevity; it just needs to work with the rest of your application to enhance the chances that you will be accepted to the program of your choice. However, Dr. Johnson's advice is still applicable. Tell your story. Get it down on paper. Then edit it until it shines.