This happened to me, pretty much.
The summer between sophomore and junior year I started experimenting with different belief systems. I had always been very religious, and shared the conservative political views of my parents. After shedding those beliefs for different ways of thinking, I applied my questioning to more than just religion and politics, to the way I viewed my life here on a tiny planet in a vast cosmos.
In the fall I began falling deeper and deeper into the existential void. The absurdity of everything is laughable. I began to occupy myself with questions: What is the purpose of life?, Why is there something rather than nothing?, How can we know anything? How can people get angry over trivial things?
Rather than do my homework at night, I’d read Nietzsche, or Herman Hesse novels, or Kirkegaard, or anything. Or I’d write in my journal, or just sit and think. This was the time I stopped watching television, and I read more during that time than ever before. I felt what I was doing was more important than school work, and, to a large extent, I think it was. It was liberating to discard the scale of importance that most people used, and simply use my own scale. To me, the most important thing one could do was contemplate life, and the universe, and all those ‘big questions’ that don’t have answers. Some of those answers can be found.
What really happened to me was this: I stopped taking my beliefs for granted. I was willing to consider any worldview, but I refused to accept any of them, because there was no certainty in any of them. I wanted truth, but the universe did not yield any answers to its secrets. I don’t think the universe knew either.
After you hit complete detachment from the common view of “the world” and laugh about it for a while, the only thing left to do is to regain that view. Slowly I started getting irritated by things that people did, rather than puzzle over them. Catching the bus on time became important again. I became normal again.
In my case it was a healthy journey, one that I am a much better person for. Once you reach the point where you can be sitting at the dinner table listening to your family talk about the most ridiculous, commonplace things as though everything in the world makes perfect sense, while you can’t even be sure of your own existence, because everything in the universe (the universe!) is so strange and amazingly complex and doesn’t explain itself, there’s nothing left to do but stare at the walls and laugh. I suggest having a long talk with your friend. See what is on her mind. Because she does sound a lot like me. I was a very quiet, straight A student, I gave up going to a lot of after school activities (except, not surprisingly, philosophy club,) and I could see Hamlet being an excellent trigger to thoughts like these.
She may simply be going through something that some people are lucky enough to go through. Before she ends up with a the label of a disease or disorder applied to her and medications that will fuck with her brain prescribed, try to find out if she’s just experimenting with a new way of looking at the world. If she’s going through the marvelous thing that I went through, it won’t last forever, and she’ll probably be herself (or an improved version of herself,) in several months time. Or maybe she isn’t going through what I went through at all, and maybe she does need help, or treatment. But, if this is what she’s going through, (it sounds quite like it to me,) she is probably right in saying that you’ll never get it. It’s something you need to experience to understand.