I understand that academics are your priority. However, your best chance by far to get in to one of the top schools you listed is as an athletic recruit. Since you were a Junior Nationals qualifier, you should be in the right range.v You might want to check out this discussion:
http://talk.collegeconfidential.com/athletic-recruits/1301331-female-swimmer-reality-check-p1.html
Yale, Harvard and UChicago are all great for politics/government. Hard to go wrong with any of them. I didn’t go to any of those schools undergrad, but I later spent 4 years at Harvard and 7 years at UChicago. Personally I preferred UChicago, both academically and socially, but that’s just my experience. I have less personal experience with Yale, though it sounds like it would probably be a good fit for you.
Chicago is a bit more interdisciplinary than Yale. It’s a bit easier to double major, and I believe there’s the possibility of doing a joint BA with an MA in International Relations, if that’s of interest to you. Chicago is a lot more interesting and cosmopolitan than New Haven.
You might also want to take a look at Duke as another option. It would probably be outside of your range as an athletic recruit, but it would be another attractive option as a school with great political science/international relations, and more accessible from an undergrad perspective than Harvard in terms of taking advantage of things like the Sanford School of public policy and civic engagement opportunities.