Those are excellent test scores – congratulations on your achievements so far! Most private schools are members of the National Association of Independent Schools (NAIS), which to my knowledge forbids schools from offering merit scholarships. I think you will be out of luck there, and your parents will just have to pay for you to attend one.
I realize your need to find academic challenge. Let me describe how my daughter found academic challenge in a public school versus a private school. She had scores like yours and was accepted to all the top private high schools in Atlanta, but the tuition was going to be very expensive. We started analyzing what the private schools offered in the way of curriculum versus the public schools. Here is what we found: the private schools typically limited students to six AP courses throughout high school, including only one AP science course. My daughter, who loves science, was horrified to discover this. She wound up attending a public magnet science high school. She took 15 AP courses, including every science and math AP course. In total, she had 8 science courses and 4 math courses in high school, plus tons of related clubs and competitions and other activities. She won international and national awards, and got lots of scholarship offers and an Ivy admission when she applied to universities (she accepted the scholarships, because money remained an issue). If she had attended one of the very expensive private high schools, she would have been so limited in her achievements and education by comparison.
Keep an open mind as to which high school can offer you the right caliber of academic challenge. Take a close look at the curriculum at each high school, and look at options among your public schools in addition to private.