Welcome to AZ.
Competition, or more precisely pressure, affects different people in different ways.
Some people fold under the pressure. Some people excel under the pressure. That is why you might hear the following expressions:
"he is a practice player". A practice player can only play good for free and usually by himself.
"money player". They, like me, play their best when there is money and pressure on the line.
And finally you have "tournament player". These guys play good in tournament type pressure, but not heads up money matches type of pressure.
Of course many people might be a combination of the above.
I'll give you an example in my case. I've been a "gambling player" all my life. It used to be $50 sets would cause me to have just the right amount of pressure to play my best when I was younger. THat progressed to 100, then 200, then 500 and more. As I got used to playing for larger amounts of money, I would no longer have the right blend of pressure and motivation for small amounts of money, and would not play my best unless the money was high. By the same token, I never did well in tournaments, cause there was no pressure on me to play my best.
On the other hand, some players play great for $5 but fold completely for $100.
These types of personalities often stay with us forever in our pool careers. But like anything else, the more you do something, the less you will feel the pressure. Your body will become accustomed to it. My advice is to keep putting yourself into the situations that cause you the most pressure. You will eventually (hopefully

) be able to handle it.
Also, knowing with high proficiency what you are doing at the table will ease the pressure on some players (but not all). I highly recommend Joe Tuckers "Guaranteed Improvement" book, no matter if you are a beginner or an A player. It is a position drill book that also has charts for you to track your progress. If you do the drills you WILL learn the shots, and you will have the confidence to know where the cue ball is going in a real game.
Another strong piece of advice I have is to read "The Inner Game of Tennis". It is a classic book about quieting your mind so it will not distract you. EVERY pool player should read it. You might even go up a speed when you get through the whole book!
Good luck.