When I started my PhD program, a group of us were given a little talk by the department secretary.
She told the story of how she went to audition for Jeopardy!, a trivia game show. She saw a whole bunch of other people at the audition get really nervous and choke up; her take on it was that they were used to being the most knowledgable in the room -- they were used to sitting in front of the TV screen with their friends or family and knowing every fact, and when they were suddenly confronted with a situation where everyone was as knowledgable as they were, they were suddenly very intimidated.
She, on the other hand, was completely relaxed -- she spent her days working with Nobel prize winners and loads of other people for whom she had no doubt were smarter than her. Being confronted with loads of people smarter than her was a daily experience.
She told this story to us to say, a lot of you will experience the same thing: You were used to being the smartest person in your High School, you were even used to being the smartest person in your classes at the prestigious university you attended. Now you'll encounter a situation where everyone is like you: the best and most driven people in your classes.
You'll feel stupid and inferior for a bit, and that's normal. Don't let it bother you. Eventually you'll notice while that most of these other people have areas where they're better than you, they have areas where you're better. And there will still be the occasional person who seems better than you at everything: that's OK too. You're not the best at everything, and you don't have to be.