Verified answer

I think your strongest case is "teacher A's class is literally 100% full and its just too many people and sometimes i feel overwhelmed" (as long as that is not also true of Teacher B) since they already said they won't do it just cuz you simply want to switch teachers. You have to convince them it goes beyond personal preference. Maybe teacher a just doesn't teach to your learning style- it's not that anything is intrinsically wrong with her, it's just that her teaching style and your learning style aren't compatible (or so you'd say). Maybe so many students gives you anxiety. But you do not want to come off as whiny or saying the teacher sucks. Getting your parents on your side and advocating for you will help a lot. Have them talk to your principal or guidance counselor if your attempts to have failed.

If it doesn't work out though, then see it as a character-building experience of learning to learn in spite of the teacher, and make the most out of a crappy situation.

Develop your case by outlining the risks for you to take the course with Teacher A. Make up a really good excuse to your parents so that they can talk with your school's guidance counselor. Then even the worst school policy is meaningless once the counselor approves the change, which he/she should. Make your case even stronger by stating that "teacher A's class is literally 100% full". You as a student have every right to stand up for yourself when it comes to academic excellence where the only roadblock is an unsuitable course instructor. Go ahead, convince your parents, meet with the guidance counselor and finalize the deal.

By the way: "cobb county (GA) policy" is garbage.