A complete answer to your question would require knowing whether you attend a state university or private university and what is provided in the university's academic policies. You seem to be asking for an opinion as to whether you should win your appeal; that depends on too many factors. A lawyer is only going to be able say what you ought to do to make the best case.
Certainly there is some unfairness in the result. You might consider that this is like the case where a scientific paper is published with many names on it and one person knew that the data was falsified but the others did not. I believe that a case like that has arisen recently at Harvard. You might look into that analogy and talk to someone in a science department at your university about how it might be handled.
One question that needs to be considered is what are the expectations for cooperative work and the obligation for each student to make sure that the entire work product is original and valid. What notice was given of the expectations by this professor?
You need to consider the possibility that someone will consider the professor's policy within the range of her discretion and how you will meet that argument.
You might go on line and see if you can find examples where the problem has been considered. There might be useful material in educational methods books concerning the use of cooperative projects. In that regard, you might try talking to someone in the education department at your university for assistance in finding materail or supporting your argument.
DISCLAIMER: I have not agreed to be your lawyer or to give you any legal advice. This response is for information purposes only and is not legal advice. For legal advice you need to find a lawyer who will agree to represent you in this matter.