Being a toddler is a very difficult thing. As our babies grow into little people, we constantly tell them what a "big" boy or girl they are as they master new skills such as using the toilet. Toddlers are, I'm increasingly convinced, in their own minds at least - mini adults! Since they have learned to walk, talk and take care of their own toilet busines -they can pretty much take care of themselves. They are invincible! When our cute little babies learn to exert their own will, throw tantrums and yell NO! at any opportunity it can be pretty scary to say the least.
Once they reach this stage it can be very hard for young children to deal with their own limtations. They can walk and reach things (especially in a supermarket) and can't yet understand why they can't have everything they see. This is I'm afraid the Age of Reason! Children need to know the WHY? of everything - this requires huge patience and a never ending supply of explanations.
Toddlers on the whole do not understand why they can't do or have everything they want. They are not yet able to see things from anyone else's point of view. This includes siblings new and old as well as parents. This is the time in a child's development when they need to understand the rules and the boundaries within their own families and in their wider world.
I have found a technique called 1,2,3, Magic to be really useful with my own daughter and have seen it used well in schools and nurseries.
Basically, when a child's behaviour is not acceptable, you tell them that you don't like that particular behavior.. You say that they have three chances - 1,2,3 - and if they reach three, they will have to go to the time out chair or step. Allow 2 minutes for a two year old, three for a three year old and so on....
Each time they display this behaviour, count them up to three. Most children learn the boundaries pretty quickly this way.
I have never used this for minor transgressions, more for children who display agressive behaviour towards others, such as shouting or screaming, smacking or other more serious behaviours.
Your daughters tantrums sound quite extreme and she appears from what you have said to be very angry and frustrated. This might work for her.
Does she only does this when she can't have her way?
If she is hurting herself, then I would advise you to visit your family doctor or health visitor for further help. Hope this helps:)