M.C.
I am no psychologist... but it sounds to me like she needs more attention. She might be feeling insecure in some way. It could be a stage (my 3 year old is going through a stage where she has "moments" and will tell us awful things like "big people think I am stupid" or "i don't love you" the more you react in anger or 'emotionally' - the more it escalates...
What has been helping with us, although she is younger... is calmly reassuring her... while STILL enforcing rules. Our daughter is testing to see where her boundaries are... she want to see if she has the sway to get her way and saying hurtful things both "tests" our love of her, and tests her ability to get her way- so far she is losing on that front.
On the other hand I do think that kids (up to teenagers) - can reach a point when the feel an emotion more strongly than they know how to express it. We use time outs here, and my daughter can scream, yell, or be mad... as long as she stays in time out. If she gets to the stage where she is sobbing and can't get a hold of herself it is definitely time to step in... tell her to take deep breaths, relax... and talk it out. She also must know that her feelings are never "wrong"- she can feel however she does... how she acts and treats others is what matters. The calmer mom is... the calmer she will be. Usually my daughter gets the most upset when she feels a complex emotion that she has trouble putting into words.
If I were to try to tackle her issue I would try prevention (try to set a positive mood at times you anticipate she may get upset... reminding her that good behavior will be rewarded, and when she does good things... take care to acknowledge them... even if they are "expected", also setting aside special time focused just on her top help satisfy her need for attention in a positive way... AND back that up with using your own calm and a sense of structure to help her work though her outbursts.
And if none of that works... book a session or two with a child/family councelor. It does not mean she or her family is dysfunctional in any way, but coucelors are trained to see the signs and root out the cause of these sorts of issues and a good one can give you incredibly useful tools!
Good Luck
-M.