Agree. If there is any way to make your current school work, I’d recommend pursuing that path. It’s very difficult to get into the best boarding schools in 11th grade, and its the most difficult year, so you risk an “out of the frying pan into the fire” situation.
You have an amazing background and if you’re fully committed to going to a US Boarding School, give it a try, but you’re doing well at your school despite your unhappiness there and you’ll be a senior next year. Develop relationships with people who will be recommending you for college in the next several months and I suspect you will have better outcomes. It’s hard enough to get into the top schools (which are the ones more likely to give aid to international students), but doing so without strong recommendations is a very very steep hill to climb, in my opinion.