I don't know how it was for you in high school, but for me failure was not an option. You did the work, you got an A. And while that's not everyone's experience, I think we'd all agree that college is DIFFERENT.
Before college, I had never gotten a B on my final grade. Ever. But when I got here, that changed--there were too many demands on my time between work and school and trying to figure out a social life. I got a B. And I didn't die. It didn't even hurt that much.
The point is, in college you're probably going to have to deal with failure, with rejection. You'll apply for internships that you don't get, you'll work really hard in a tought class and still come out with a B, you'll try to balance sleep and work and food and school and sometimes you will fail (I'm writing this on 3 hours of sleep, for instance).
So how do you go on? In the face of weekly rejection letters from literary magazines and my mounting fear that no grad school will want me, here's the system I've worked out for somehow staying sane and pushing forward, even in the face of rejection.
1) Be Positive
This means two things--first, it means to stay positive. Yes, that's easier said than done, but occasionally reminding yourself that you don't suck (even if you don't believe it at the moment) can really help you stay sane. Secondly, it means to be positive about what you're going for. If you truly want something, it doesn't matter how many times someone tells you no--you'll be able to keep pushing forward because you know it'll be worth it when you're finally successful.
2) Always Give It All You've Got
It's a lot easier to deal with a bad grade or a rejection letter if you know you did the best you could. Earning a B with hard work is a very different story than getting one because you just didn't put in the full effort it would have taken to get the A.