Student or Learner
My school is a school where students' age ranges from 13 to 18. So can this be called a middle school or a high school from a native's point of view? Or is it different in USA or in the UK or in Australia?
"High school," in the US would be the final 4 grades. Students would be 14-18 years old. So I would use "high school" in your situation.
"Middle school" is between elementary school and high school. Usually grades 6-8, ages 11-14.
Perhaps you could call it a junior/senior high school. But I wouldn't object to calling it a "high school" even if the youngest children were younger than traditional high school students.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.