Do you mean you are a grad student (master's degree) in cello performance?  If so, I am of the opinion that you should have developed some coping devices during your undergraduate years.  If your field of study is something else and you are taking cello classes for pleasure, I would agree that you need a different teacher.  Stress can become ingrained over time, and if you are playing for pleasure it can mar the experience.  But as I said already if you are a student of cello performance you need to develop some coping devices for criticism because it will always be there, and it won't be sugar coated.  I would suggest a counselor who specializes in CBT therapy.It has helped many people get through the stress of modern life.