You seem like an amazing young man! I think it’s so impressive that you did so well in the ISEE without English as your first language, and that you have apparently adapted so successfully to an entirely different country, culture and school.
That being said, I think you probably know that the acceptance rates are low at the trio of schools you mentioned. Most candidates are qualified, and even then, only 10% to perhaps 15% of applicants are accepted. Many factors play into an applicant’s chances, including athletic ability and the need for financial aid (at Choate and Lawrenceville, though not Andover), but especially the potential to thrive in and contribute to the school community. Personally, I think your compelling personal story, as well as the impression that you are a nice person, will come across and increase your chances a bit above the average. However, even if your chances increase by five percentage points, they are still low in absolute terms.
I also wonder: if you went from 6th grade to 8th grade, perhaps you are quite young to leave your family to attend school halfway around the world!