I have some experience about that, and I can tell it's gonna be fine.
In my country, the tough, competitive, stressful years are the two years following high school. You have to attend a very hard preparatory program before taking competitive exams toward elite schools.
When I started the prep program, I indeed thought I would be crushed. I thought my fellows were genius. Finally I got over it. It wasn't always fun, but I survived. And the others were just like me.
After that, I got into a famous school, and me too I thought there had been a mistake, and one day someone would tell me: "I'm really sorry, but the school has just realized there was a mistake with your admission", and crazy stuff like that. Now I remember that, it seems totally bulls***. And again I thought I would seem so stupid compared to the others, but no. I did well, not perfect but not bad either.
This is my own experience, but I know many, many people who were just like me. Of course some fail, but frankly they were ALWAYS those who couldn't care less about what they were doing, who didn't work, and so on. So if you are interested in your program, and willing to work (I don't mean being a workaholic, just working seriously), there's no way you can fail.
Now I am about to go to grad school, my main concern is rather leaving my country to live far away for five years... Everyone's afraid of something.
Good luck everyone!