I am scared to play a Normal Game of League of Legends. Can someone help?

Sounds like some sort of anxiety. One thing you should keep in mind is that no matter how good you are, EVERYBODY loses a few :) On top of that, EVERYBODY makes mistakes. I can guarantee you that you are no different. But if no mistakes are made, then no lessons are learned so it's a good thing! If you're that concerned, I would recommend starting a new summoner account and playing with some level 1s. If you do well, it may boost your self-confidence in this area thus reducing your anxiety. If you do poorly, you will not hurt your account and will remain anonymous so no harm done! :)