Is it normal?First of all, yes, you're perfectly normal! Don't let anyone tell you otherwise. Being scared, fearful or nervous is a natural process, and always has a logical reason behind it. It happens to a lot of people, trust me. Your mind works as a reflection of your perceived life experience.
Why does it happen?It's all about self-perception, because others see you how you see yourself. Being nervous is all about fear. But what are you fearing? You fear that people won't like you or see you for who you really are. And this fear usually derives from the self, being that you are not reaching your full-potential, and such social events as you have described, possibly remind you of this underlying conflict you have with yourself. And it is a conflict that you must learn to rid yourself of. However, in your mind, right now, I want you to thank those people who have brought this attention to you (including those girls who made you feel terrified) because with this shift of focus, you can improve yourself and improve your perception of who you are. These people making you feel this way are actually helping you to understand yourself, or more accurately speaking, your current perception of yourself and what's wrong with it. Try to see this as a positive thing.
Can it be broken?The simple answer is yes. You can transform yourself and make dramatic changes in your life by improving the way you perceive. Changing the way you perceive, ultimately changes everything about how you behave and react to external stimuli, including your tone of voice, your body language, facial expressions, the processing rate of your brain, since all of these things can be overriden by fear.
So how do you elimatate the fear? Start by breaking your self-image. Sounds ridiculous? Trust me, try this. Laugh about it. Laugh about the fact you keep getting yourself in nervous wrecks. Try to see the funny side in this. And the reason you can laugh, is because you're not actually laughing at yourself, you're laughing at how you sometimes behave. And how you behave is a mere reflection of your mindset, it has nothing to do with your actual personality.
Also, you must try to stop caring what other people think. Easier said that done, but try this. Next time you feel scared by a person, think about how you perceive them instead of how they perceive you. Think to yourself, "do I like this person?" and "are they worthy of my time?". Even if you don't feel it, get yourself in the habit of it, because how you feel and think is important, and you must give credit to yourself.
The last thing to do, is to get rid of your ego. Destroy it, completely. That is, the thing that makes you desire in order to satisfy your perception of your self-worth. You're potentially a very powerful person who just doesn't know how to use his power. So start using it. And accept what you don't have, and if life brings you good things, be grateful for it. If you spend too much time building expactations in life, and then get upset about those expectations not being met, then you will always be lacking. If you just accept yourself, the things you do and don't have, and realize that this is just an experience, then you can never feel dissapointed.
Good luck
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