Well, if you're female, it can partly be due to PMS. But even if you're male or female, most likely at this age, your hormones are still all over the place. Moodiness is not uncommon, and these problems can still be due to being young and confused, even if you are older.
The cutting feeling... be careful with that. Mine merely started out as a urge, with tracing cuts, but nothing lasting. And then I let it progress. I was never a heavy cutter, but even after about 2 years now, I do have two marks that have yet to go away.
It's really all in you... what was most confusing to me was knowing that I didn't have these ~horrible~ problems, and yet they were still tearing me apart.
When you get into that feeling, try doing something to change it, or at least counter act it. Do you play an instrument? Sometimes playing when you're upset helps... listening to music (whether you want to do something upbeat to counter it, or something more "depressing" to let you vent your emotions through it). Personally, I liked taking a cold shower... it really woke me and gave me a few moments truly to myself...
All in all, in terms of needing to feel that pain. You can always go out and do something like exercise. Running, a long walk, playing a sport... it could help you with that, if you don't already to so...
I wish I could help you out, but just give it time. Since about 10 years old, I can remember thinking about suicide. It wasn't something that big, but I couldn't be on the second floor of a mall without at least thinking once about jumping down.
Around 16, I got worse, and started cutting, and hit some of my lowest points. And around 17 things turned around as there was a bit more clarity in my life (knew where I was going, what I wanted to do, etc). So while it's not very helpful, all I can really say is to hold in there! Very typical, I know, but that's really how it goes. Find something that works for you. Reading, writing, painting, music, cold shower, hot shower, sports, running, walking, cleaning... who knows... and at least see if during some of your lower times, you can find something that can distract you. More than anything, being alone makes those overwhelming feelings of self-harm come into play. So if you feel it... go sit in a room with someone else there, you don't even need to talk to them. Go chat with someone, call up a friend, even talk to someone via internet... or just go out for a walk in a park where maybe there will be other people. It may make a difference, you never know :).