I used to be that way too.  One thing to think about that might help is even if you do look stupid for a second nobody is going to remember 10 minutes from then.  Another thing that helped me was thinking about how good it felt if a stranger started talking with me in public for a 2-5 minute conversation and how it didnt upset me or make them look stupid so I shouldnt look stupid if I did the same thing.
That's true... the anxiety goes away immediately afterwards!