Also, you can't be "a fool" for believing in yourself. Confidence, false or earned, is incredibly useful in motivating yourself to push limits and achieve great things. I have found that as long as I tell myself my goals are achievable and do my work in that mindset, I can do many things I thought were out of my reach. It sounds like "The Secret"-esque bullshit, but it can help.
There is no reason to push yourself to the point of "breaking as you describe. When you get there, take a step back and think about why you're at school and why you're chasing x or y career goal. The point of work is to purchase leisure, but if you're letting work consume everything then you'll have a hard time being happy. I think many people forget that work is, in many cases, a means to an end. Slow down until you're at a point where you can enjoy your time, and don't worry about the pace of everyone around you. Again this might sound like cliché nonsense but I take a lot of comfort in thinking about the big picture when pressure builds.
If you weren't looking for advice, forget everything I said. Also I congratulate you for "letting it all out", it's not easy to compose one's thoughts into such a rational assessment of a bad situation.