I dreaded the same thing in school, even at work now I dread any kind of attention coming my way. What can be helpful to some people, is breathing deeply. When you breathe, in through the nose, out through the mouth, and expand your stomach, not the chest.
How long is the poem? Try not to rush through it, read slowly and concentrate on the words, not their eyes. I know it's easier said than done, just try.
Let me know how it goes.