You have a good unweighted GPA. I'm not entirely sure how your school calculates weighted GPA (A in honors is 5 is they way we were taught), but I would like to see a description of your current and past coursework. Good class rank, within top 10.
Your SATs are fine and you've already taken them three times. Did you use your highest scores? If you didn't, then there's a chance for you to improve without having to retake.
Good AP classes, self-study doesn't mean you get honors credit though and it doesn't appear on your transcript for Cornell to see. It's good to see you're keeping up hard senior coursework, do not fall prey to Senioritis.
Those are good SAT II's, If you're majoring in any of the Sciences, you might want to take a test in one of those as well.
Your clubs are solid. I don't see anything completely out of the norm, but if you have had several years of participation, then you will be good to go. Good leadership positions. Think you can secure an internship at that hospital? Mention your sports too.
I'm just going to sum up the rest in this paragraph since there's so much. You've got a good chance, make sure to mention the research project. Just keep those grades up and hope for the best.