If the administration knows about it and hasn’t bitchslapped the professor, then I weep for your school.
Last resort: write/publish an opinion column in the school newspaper, explaining exactly what happened and why you feel you’re being treated unfairly. I know the test was small, but at this point it’s the principle that matters: you followed all the rules and still got treated badly, and the professor deserves to have the weight of public opinion brought to bear against him.
I give open book, open-note multiple choice exams. However, I write my own questions and I’m pretty good at creating tests, even multiple choice, that require synthesis of the material. When students fail one of these (and a few always do), it’s really clear that they didn’t put much effort into it.
Because I’m interested in whether they can retrieve the correct answer, not whether they’ve memorized.
I use other kinds of assessment for other purposes.