First let me state that everything I am going to say is from my own experience as someone that was exactly like your girlfriend not so long ago.
I think that the best for you would be to break up. Your girlfriend is clearly overly possessive, somewhat manipulative, and potentially dangerous. But, if you really want to make things better, there's a few things that could help.
(A) Professional help
Like @Anne Daunted asked: did you look for professional help? If not, then it is a very good idea to look into it. A professional might recognise symptoms of a potential disorder, and/or help you and her control those reactions.
Most of the time, a girlfriend threatening to kill herself will not do it. But there is always a slim possibility. That is where a professional can tell the difference between possessive behavior, and dangerous behavior.
(B) Assert yourself
I think that in a relationship, once "roles" have been established it becomes extremely hard to move out of those "roles", because the relationship is building up itself on those.
That's why it is important to be careful to create a healthy basis for a relationship from the start. Things like Respect, Communication, and Honesty are extremely important in a relationship, and I think yours is lacking at least two of them:
Respect: She does not respect you, she treats you as if you belong to her, and while it is what some people want from a relationship, it is also not what you seem to be looking for. She calls you at any time of the night, meaning that, for her, you should always be ready to answer her, she threatens you, so that you go home to her. If you can't attend the plan she makes, she ignores you. She does not treat you as a human being, for her, you should plan your life according to hers.
In a relationship, both parties should be equals, if you want to avoid a situation like this in the future, make sure that the other person treats you with respect, and that you treat them the same way.
Communication: Obviously there is a lack of communication, I think that both of you are expecting different things from a relationship. She is planning things without asking you, and getting angry if you can't attend. When a couple or a group is planning something, everyone should be involved in the planning (unless it is a surprise, or something like a bachelor party of course).
If you want to avoid such a situation, you should make sure that both parties are involved in the planning. Also, you might need to make clear what you're looking for in a relationship when you start dating. Not everyone has the same view of what a relationship means.
(C) Another piece of advice
There is many professionals that help people when it comes to relationships, there is of course, couple therapy, for those already in a relation, but there are also some professionals that can help people find a partner that corresponds to them better. You might want to look into that if you find that you often fall in relationship that doesn't suit you.
My advice regarding what you should do:
You are currently in a relationship, which does not make you happy. Moreover this relationship is putting a lot of stress and pressure on yourself. I understand that you care for her and do not want to harm her. I have been like your girlfriend, I was the clingy one, the demanding one, I was desperate for my girlfriend's attention, and would resort to petty tricks to get it.
So from my own experience, I believe that the best solution would be to have a long, and clear discussion with her. Telling her how and why she is causing you a lot of problems, and that you need her to stop. You need to be as honest as possible, but also need to make it clear that you can't take this anymore, you are not her pet. If that doesn't help, then I would advise in breaking up.
I hope this might help you a little.
If you worry about her suicide threats, something that should be looked into is Preventions Hotline (they might change depending on your country). Those hotlines can help you deal with a potential suicidal person, and it can also give you insight on those threats, you can also contact them by chat if I remember correctly.
As stated by @Tycho'sNose: Crisis hotlines might be better suited for that kind of situation.