Even though your school doesn’t rank, will the college have ANY idea of where that 3.77 puts you in your class? Many schools that don’t rank will send an accompanying letter explaining what percentile of the class a certain range of GPAs would be. If your GPA puts you in the top quarter of the class, with your SAT score and your ECs, and if you classify yourself as Latina, I think you do have a chance at getting into Harvard and Georgetown.
I wouldn’t worry so much about all the legacies at your school, unless their ECs and GPA are better than yours. Seems as if slightly less than top-rated legacy students are often getting a soft rejection (meaning wait-listed). Your URM status (if you classify yourself as Latina) will help at least as much as their legacy status. Also, legacy status only counts at one or two schools. Athletes can only accept one school. Latina will help you everywhere.
I agree with all that has been said. Don’t submit the ACT. Do try to emphasize your math and science, especially that you’re interested in Physics. In fact, tell schools that you are waivering between IR and Physics, as to which will be your major, and which your minor. I think that at Harvard, you’re more attractive as a woman interested in Physics, than in IR. From your record, I think that IR at Georgetown is your best match.
Apply early action to the one of these that you most want to attend, and in the application, let them know exactly why you intend to go there, what you intend to study, why you want them so badly. Unfortunately, I think that your highest chance of admission to one of these two is if you apply early action to Georgetown, which will mean putting yourself in the regular decision pool for Harvard, which cuts your chances there in half. Show a lot of interest. Contact the teachers whom you want recommendations from now, early on. Cultivate a relationship with your school advisor who will be writing your cover letter.
Can you do a research project this summer with a Harvard or Georgetown faculty member, who might then write an additional letter of recommendation? It can really help if you have a supplemental letter (for a real reason, not just an “I know the family” reason) from faculty at the school. If a faculty member wants you, it can move you from the “Why should we take this person” pile, into the “Faculty member wants her. Can we take her?” pile.