Is sleep necessary?

Do our bodies depend on how much sleep we get?

I haven't been to sleep since yesterday morning. As soon as I got up, i caught up on some homework and studied for a good 5 hours. After that i went to the gym and worked out for 2 hours. Then, I came home and did more school work. After that I worked an 8 hour shift and now my body is feeling heavy and numb. I haven't slept in about 24+ hours. I feel like I'm stuck or paralyzed.