How does transferring work where you live?
In my town, kids can attend the HS of a neighboring town- but there is a fee associated with it. Cheaper than private school, but if you don’t attend in-district, you pay for it. You can attend the HS on the other side of town without a fee, but the district office needs to approve it (they don’t want every single female student at one school and all the males at the other; they need to make sure both HS’s are operating efficiently with a critical mass of students, etc.)
How would the logistics work and have you discussed your plan with your parents?