The title says it all I guess, but I'll give a bit of a rundown.

Last year I started seeing a girl long distance, she lives 950km away from me, so we could really only see each other once a month. When we weren't seeing each other, we were calling each other, texting each other, sending letters, talking online etc.
But after a while and a lot of other complications, this got to be too much for me, so I broke up with her after three months, which seemed to devastate her.

We actually decided to stay friends afterwards, and things were mostly going well for a while, I was moving on with my life, I started to hang out with my friends again, pick up the things that I had put on hold for her, but then she got heavily depressed.
She gets really upset and angry every time I hang out with a friend, she's even gone as far as to tell me that I'm not allowed to go to parties or hang out with friends at night because she's afraid I'll get drunk (she hates drinking) and because she gets extra lonely at night.
I went to a close friend's 21st birthday a little while ago, the entire night she flooded my phone with texts asking me when I was coming home, saying she urgently needs help. I ended up going home early (this was the first night I had gone to a party in ages) and when I got there she threatened me with suicide and said that she was close to killing herself that day. She went into detail about how she was going to do it and where she was going to do it, things like that, the entire time I felt completely sick to my stomach.
What I should've done is called her home number and blown the whistle on her to her parents, they could at least help more considering I live so far away. But the stupid thing is that I know if I did that, she'd probably stop talking to me all together and I'd lose a friend which isn't what I want.

But lately I've been thinking I don't have much of a choice. Unless I do exactly what she wants, stay home and talk to her constantly, then she gets really upset and depressed and talks about suicide and self harm. Last night she told me that I was the only thing that was keeping her going and that without me she'd probably just give up and wouldn't bother going on with her life, which scared me.

A part of me thinks that maybe she's just manipulating me and blackmailing me into doing what she wants, and that if I were to cut her off, block her from everything and change phone numbers, that she would be really angry and upset, but she wouldn't do anything.
But then another part of me is scared that she might do something, and I don't want to deal with that kind of guilt because I'd feel entirely responsible if she did something to herself.
If I can't talk some sense into her like I've been trying to, then I think the only thing I can do is call her parents and tell them?

Has anyone been through this sort of thing before that can share some insight? I don't want to lose a friend, but then if she's threatening me with this sort of thing all the time then I don't know if I have much of a choice.
Any advice would be greatly appreciated.