So I took a pre calc course over the summer with a different high school than the one I'm attending. Do I have to put the class in with the school as a summer course or do I just put the class with my school as my school put the class as a "transferred" class on my transcript
You can do it either way and it since what you are working on is the self-submitted transcript of coursework and grades. Since your HS has treated the class as a transfer credit of coursework and grade, the college admissions office will see that on the official transcript. If you put it down as a summer class it will probably make more sense to them when they compare it to the official transcript.