Hi M.,
We went thru similar with our second child. My husband's cousin, a mother and step-mom of 9 children, said what she finally had to do with one of her very head-strong young daughters was to bodily wrap herself around her daughter when her tantrums got too violent, restraining her arms and keeping out of the way of her teeth. She found it best to carry her in to the bed and hold on to her there to prevent injury, restraining her gently but firmly until she calmed down to talk about it and have a hug after the storm. This gives her a safe environment until the tantrum passes, and shows her that she you are both there to help her and that you are in charge. Yes, it takes alot of stamina to hold onto a child in that kind of tantrum, but there aren't alot of other choices when it gets to the point that they could get injured. In all liklihood, it is just a phase and will pass. It's very frustrating for some children when they can't yet communicate clearly what they want or are upset about.
It's probably also a very good idea to visit your pediatrician to make sure she doesn't have an ear or sinus infection. Sometimes children act out horribly when they are in discomfort but can't verbalize it. (Even since speaking age, often my kids don't tell me when they have earaches or sinus discomfort, they suffer but forget to TELL me!).
Also worth seriously considering: Keep track of what she eats for a few weeks to see if there is a correlation between something she is eating and the outbursts. Intolerance reactions to foods can happen from 10 minutes to 48 hours after eating. (Intolerance is not the same as an allergy that causes hives.) One of my sons goes berserk if he eats anything with red or blue food color, the other goes berserk if he eats anything containing MSG (both of which are surprisingly in TONS of grocery store foods...). The MSG kid also gets beet-red ears and mooodswings if he eats anything with corn syrup, again which is in most every single food product at the grocery store. Many kids are intolerant to cow milk, wheat,soy, corn/corn syrup, food dyes, etc. Many kids are also intolerant to otherwise healthy foods that naturally contain salicylates, such as apples, grapes, and strawberries. You can find out more about that online: Dr. Ben Feingold, MD was a pediatrician/allergist who specialized in linking diet to behavior problems in children.
Wish you the very best getting through the tantrums, keep taking deep breaths, and it's OK to cry!
C. N.