One trick I learned, similar to another poster, is to look at the bridge of someones nose as you speak to them.
They have no idea that you are doing it and it is closer to their eyes but without actually looking into their eyes.
Ask yourself the question "if I did look into their eyes... what would that mean? What would be so bad about that?"
Once we start to realise the reasons behind why we avoid something, we can begin to work on them.
I used be terrified at getting up and talking to people in a group, I even used avoidance (phone in sick etc).
However, when I looked into it, it was about what other people thought about me and how they may judge me. I too was a painfully shy child.
But I learned that people are entitled to their opinions, I couldn't mind read so I couldn't know what they were thinking anyway. I realsised that it wasn't them that was the problem, it was the way I thought about them that was the problem.
Once I worked on this all became fine and I can talk to anyone now and often give presentations to large groups.
Cognitive Behavioral therapy is very good at altering your thoughts and beliefs. If you can't afford to see a therapist I would recommend a self help book written in the CBT style.
It will help you address your thoughts and beliefs about the situation which causes you distress.
I wish you all the best of luck... If I can change, then anyone can!
Regards
Chris