First, seriously, go see a therapist before you make any decisions. The fact that this is happening during your freshman year is disgustingly normal - everybody goes through a period of adjustment at this point in their lives, but it's much harder for some (particularly kids who have parents with big expectations).
Second, you'll survive and probably do just fine if you drop out and self-study. Having said that, an ivy league education opens doors. I dropped out my senior year. I'm doing fine financially, but I'm certain that I could have done much more interesting things if I'd stuck it out.
No, and I didn't even do anything in my field of study. I feel like I've done well despite the lack of paper, but as the years have worn on, my reasons for dropping out sound less and less credible and more and more like excuses. It's definitely a hindrance in interviews.
You may also want to consider the possibility of transferring to another school rather than dropping out.
Second, you'll survive and probably do just fine if you drop out and self-study. Having said that, an ivy league education opens doors. I dropped out my senior year. I'm doing fine financially, but I'm certain that I could have done much more interesting things if I'd stuck it out.
Remember, your education is for you.