I wouldn't think you would have to have a very close relationship with a professor, henrietta. I was a professor, and I would have taken a student's word about needing help. You might go first to the medical clinic on campus and tell the nurse there you are needing/wanting help, too.
Here in the U.S. we have mental health clinics. They take people based on what they can pay. That might be a great place to start. It might take a bit to get an appointment, but hang in there!
I held off seeing a therapist for a long time, but I am so glad I finally went. It has made a world of difference in my life.