These things hit everybody. They don't even go away when you have a girlfriend or are in a relationship. The types of thoughts you might get are just different, they go like this:
1) Is she really into me or am I wasting my time with her?
2) This is too good to be true. Will this last?
3) She did not pick up the phone? I wonder what she's up to.
4) She did not reply to my email yet. I wonder if I should call her or continue waiting?
5) Why aren't we taking photos together? Is she introducing me to her friends? How are they reacting to us together?
I just want you to know having experienced both sides that these types of negative thoughts you might be getting now do not simply go away unless you have some crazy in love girl with you that showers you with love every day....but then again, even scenarios like that are suspect because a girl that's too interested too fast can also turn just as fast.
There are allot of dynamics with these things. The best thing to do is understand, the type of negative thoughts you are experiencing now, or when they hit you, is not as bad as compared to when you are in a relationship where you have invested time, money, emotions and mental energy into it and STILL feel insecure about the girl. Right now you have simple thoughts, but you are young, free and have your whole life ahead of you still.