I have been through every aspect of this, more than once (my children are 14, 11, and 7), so I offer these suggestions, which may or may not work for your situation, but are worth a try.
First, the reasons for this could be many, her age, her personality, her reaction to her sibling who is now developing a personality of her own (and getting attention of her own that doesn't revolve around simply taking care of her needs).
My suggestions to you is to remain calm. This is the most difficult part of the whole thing (it is really hard not to react), but if you come unraveled every time she throw a fit, then you are both in the same boat. Someone has to be in control, especially when the other person is so out of control.
Next, let your action fit the behavior. If she is using bad words, simply say that you cannot hear ANYTHING that she says when she uses words like that. She will have to repeat what she is saying, minus the bad words, if she would like you to hear and respond. Same goes for whining. If she is throwing a fit, let her know that you'd be happy to talk to her, once she pulls herself together, and walk away, if you are at home. In public, remove her from the situation, and explain that she cannot return to this place, whatever it is, the store, a restaurant, playgroup, etc., until she can control herself, and then DON'T GO for a week or so. Then try again, reminding her of this as a second chance. If she does it again, extend the time of not going. Repeat as long as necessary.
Lastly, if she is throwing her belongings at you during the fits (I had one who did this), throw the things away. Seems harsh, but really works. I told the child that if you throw things at me, you must no longer want them, so they are garbage. Some things (like happy meal toys, etc.) truly went in the trash. Other toys that I wanted to pass on to younger siblings later, went in a different trash bag that went into the attic, but in either case, they no longer belonged to the person who threw them.
These things are really hard to do, because they sometimes require you to give up something that you want to do...be at the store, or a restaurant, or just have some time to do something for yourself. It probably won't work instantly, consistenty is the key. Once she realizes that you're not wavering, she will have to change her behavior in order to get what she wants.