Well, what I would suggest is finding a good steady confessor. If you get comfortable with one confessor, it might make you less fearful.
Another thing I might suggest is facing the priest, meaning not going behind the screen. I totally understand that this makes a person very uncomfortable, but it might help you in that you can face your fear of the sacrament head on. Remember, even if the priest knows who you are, he cannot tell anyone about your sins, and that whatever you confess remains in the confessional.
Perhaps you can also focus not so much on your fear of the sacrament but instead about how you will feel afterwards. I know whenever I go to confession, it makes me much more joyful and gives me a feeling of freedom. If you focus more on yearning for that feeling and that holiness, the fear and pain of going through Confession may lessen somewhat.