So far the answers have been mainly about medical issues, physiological issues, and whether or not the child is spoiled (which are all valid).
Do you and or your husband yell at each other in front of her or scream at her? Do you find yourself thinking that she acts "just like her father" ? If the answer is yes, I would consider that she acts this way because it is how you have taught her it is normal to behave. I'm not implying that you DO these things, just that if you do, you and your husband may be culpable for this issue. You can't expect a child (or teen) to handle everyday disappointments with maturity and reasonableness if they are constantly offered screaming and irrationality as the solution to trivial problems. You say that "everything sets her off". I ask you, does everything also set off you or your husband?
I can think of many example of people I've known that as children or teens acted this way. But the reasons are so varied there is no one box they can all be placed in.
I had a friend who had a dad that used to beat him - low and behold my friend had an explosive temper.
My wife had a horrible hormone imbalance that cause her to act this way that we didn't figure out until she went on birth control pills and her temper was magnified ten fold. The hormone imbalance went away after having our son.
A friend of mine has a son (13) who acts this way but he has Asperger's.
I acted this way because my mother was a detached suicidal Schizophrenic and my father was a drill Sargent. I literally knew no other way to deal with my emotions about all the bad things I had seen, which manifest in outbursts for trivial problems.
An ex-girlfriend of mine (and especially her sister) both acted like this (screaming constantly, arguing with everything, fighting multiple times a day) because their parents never punished them in anyway for bad behavior. The were entitled spoiled rotten and really unintelligent. I truly believe that simply being so unintelligent can cause this as it is such a primal way to act. If someone isn't smart enough to comprehend right/wrong in a way that takes others feeling into account, and they have never seen a punishment for acting this way, how could they possibly be any other way? I know this sounds harsh, but my ex-girlfriend hated reading, openly disliked everything about knowledge, and her parents just always told her she was an intelligent, smart, and strong young woman. Nothing could have been further from the truth. Fifteen years later, guess what? She is still like this. Can't keep a relationship, is always angry. Her sister grew out of it though. He sister also went to college.
Human tends to learn to do what works. I suggest, that she only has a problem if she has consistently not gained anything from acting like this. If she (the majority of the time) has gotten what she wants from acting like this, she doesn't have a problem, you do.
I hope you find some solution for everyone's sake.