Should I transfer high schools?

You should also consider that by transferring to a different school you are gaining some experience of how the real world is like. You will eventually need to break out of your comfort zone to experience new things. If you've never worked with boys and girls before, you will have a hard time adjusting to the real world work place that is made up of men and women. Private school is nice for certain things, but public school is a more realistic sample of the people you will later have to work with.