Your chances without being a recruited athlete are currently on the lowish side. Your 2160 SAT I is on the low side of the 25-75% range for UChicago (2100-2350 range). Your GPA is solid, though I’m not sure that your curriculum is that strong compared to other applicants for those schools. Your ECs are focused mainly on swimming and volunteer activities, so swimming is going to count for a lot.
If you are a recruited athlete, however, your chances go up dramatically. Ivies and other top colleges generally use the Academic Index when evaluating whether recruited athletes fit within their academic parameters. You can find it here:
http://www.collegeconfidential.com/academic_index_calculator/
You don’t mention your class size, but using a class size of 300 and top 10% plus the scores that you reported, I calculate your current AI as 209.5 (out of a perfect 240). That’s right on the edge of where you want to be to look really attractive academically, as a recruited athlete.
http://www.tier1athletics.org/2013/03/22/harvard-academic-standards-for-athletes/
http://www.tier1athletics.org/2012/11/05/interpreting-the-academic-index-number/
The more attractive you are as an athletic recruit, the less high your AI needs to be, as long as it meets the accepted standard (176 is the bottom end cutoff), but for someone like you who is not a top recruit, the higher the better. So getting your SAT I and II scores up would definitely help make the case. Beyond that, it depends on whether the coach wants to recruit you.
Yale is notorious for recruiting less athletes than other Ivies, a policy started by former president Richard Levin:
http://yaledailynews.com/blog/2011/09/22/up-close-elis-beat-recruiting-cap/
Chicago as a DIII school is going to be less competitive than DI Ivies. Berkeley is in another galaxy altogether, but not high on your list.
I think it comes down to a calculus of how badly you want Yale, how much interest you can get from the coach to recruit you, and how much higher you can get your AI. If the coach wants you and you improve a few spots, there’s no reason you can’t get in to Yale. On the other hand, Chicago is just as good a school (better in many areas), and the coach really wants you.
What’s also unclear in all of this is what your interests and personality are like, and how these different schools might fit you. That’s definitely something to think about.