I teach at the college level, and I would NEVER give one student's work to another, or post their work without their express permission. Sometimes a student will write an exceptional paper, and I would ask their permission to post it as such for the benefit of the other students. (No one has ever said no, but I would certainly respect it if they did!) Sometimes I require that students do a peer review, wherein they exchange papers and give feedback. (Each paper is on a different topic, so there's no chance of plagiarizing.) The works are never finished in this case, but are "in-progress", and they exchange in groups of three not with the whole class. Since they exchange with each other what are essentially rough drafts, it has never been a problem.
I agree with the other posters that you should have a very direct and explicit (but respectful) conversation with your professor, perhaps with one or two other students who feel similarly. Go to her office hours or make an appointment. You could also send a respectfully worded email. I also agree that if the professor does not agree to cease distributing your work, you should definitely take it up with the chair of the department or even the Dean of Students.