Falsely accused of plagiarism by instructor. what should I do?

Your problem is with the university, not with law. There is no universal law about internal discipline in Universities, or grading, or working together, or plagiarism. If the school wants to record that you two worked together so closely that your papers were indistinguishable, and if the school wants to record that is prohibited by school rules, no law prevents the school from making that record.