Story structure is kind of like the armature in a sculpture; it lends form and prevents it from collapsing.
I'm not a genius, but some people are. They can just sit down and write without any structure at all, and their stories don't collapse.
But mine do, and so do most people's. Story structure, for me, is like the bones. It holds the whole thing up.
Incidentally, structure is not the same as essay format. There is no set format for a college essay. It's not like an academic assignment with a rubric, an expected number of paragraphs, etc.
The idea that your personal statement can be more free-form might present challenges, however. That's why I suggest paying attention to the structure of your story.
Once you have a basic structure, you can express unlimited creativity in your personal statement. This is about crafting an essay that grabs your reader and holds them.
You build it with what Robert McKee calls a "step outline." This is a sequence of ideas or images, like stones on a path.
First, I'll say this (Step 1). It'll plant the main image or idea in the reader's mind.
Then I'll take it here (Step 2), then here (Step 3), building on the central ideas.
Then I'll say this (Step 4) to set up my ending, then tie it all together with this (Step 5).
Take that step outline and tell the story to someone before you write it.
Rework it until they really lean in. Move your steps around until you have a structure that maximizes the impact of the story you tell. Then write it down.
Not fancy prose. Just words. Once that's done, then start editing to create real verbal beauty. All great writing is re-writing anyway, so don't even try to get it perfect in the first draft.
It's the ideas that will make your essay strong, not the words.
Try it out, and let me know how it goes.