Your school most likely has an administrative review process. Ask your parents to inquire about the process and trigger an admin review. But the teacher does not have to "prove" the accusation. If school officials in the admin process concur with the teacher, based on a review of the two papers, that's it. No further proof required.
Whatever the school says, goes. Whatever grievance or appeals process the school is willing to allow is what you get.
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Ms. McCall is absolutely correct. Your best course will be to use the appeals process and ask to see all of the tests for the entire class. Make sure you ask that they redact the names of the other students as they will not give you nay "confidential" information. If you can show that a number of people had similar questions. If you have say 25 people in class but only your answers are similar, then you will have problems proving your case.