Bob, what you're experiencing is pressure. People in an archery tournament may experience similar pressure, as some people might if they have to make a business presentation in front of a group, or perhaps someone who would like to ask a girl out on a date. If it helps you any, psychologists have shown that nobody performs their best under pressure. People say they do, but they don't. Your tongue gets tied in front of a group, you sound like an idiot in front of the girl, or all your normal brain/body connections that work so well when you're practicing a shot somehow get disconnected.
Some people do perform better if they are competing, but if they do, it's because competing is a positive experience for them, and not one that causes them to feel pressure. What causes pressure for one person might not cause pressure for the next.
If you are feeling pressure in any of the situations I mentioned above, or a lot of situations I didn't mention, you can't wish it away. Accept it, and promise yourself that you'll do the best you can, which probably won't be as good as the best you could possibly do. All the advice above is good. The more you expose yourself to pressure situations, the better you'll be able to deal with them.