I agree with Perna, who has given very good advice. Schools have rules you may not know about that may put this professor in a bind and end up making a bigger deal out of it than you imagine. Going to the counseling center is confidential and the appropriate place to take this. A professor might truly care, but they can't help you and might have to tell someone if they get worried. You can always return to the professor after some sessions and let her know what happened. I think the counselors would help you much more anyway because that's what they are trained to do.