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Shit. I just sent in applications to UChicago and UVA but forgot to include the Why X essays I spent so much time writing. Should I ask them to add it in, or would it look worse to show them I carelessly forgot to do something like that? I'm also missing my school for study abroad - I entered it in one app and thought it would carry over, but it didn't.

I think you're overreacting a bit. It would have been careless if you hadn't submitted a required item like your resume. Just send them an email and ask if you can supplement your file with an additional item, and attach the why statement. No big deal.