T.B.
I went back and read this after I typed it and I am sorry it is so long but this is a subject that I seem to have some experience with.
I have heard of this from parents at the day care I work in. It is hard to be in that position, as I have been there with my older children (especially my oldest daughter). What I ended up having to do with her was to ignore her and tell her that the tears were not going to get her what she wanted. I like that you are working on teaching her to clap her hands when she is angry, it gives her another way to deal with her frustration. It sounds to me like she is definitely going into that "terrific two's" stage, and no it is not too early for that stage. She sounds like a very strong willed child and this may take some work, but you will get through it...we all do.
The first thing that I would do in your position is when a tantrum starts, explain to her that her squealing and crying is not going to get her what she wants and then immediately remover her from the situation. She has to learn this now, before she gets older and it really becomes a problem. Do you have a specific spot for your little one to sit in during time out? If not, I would come up with a place that is out of the flow of traffic in your house, but somewhere where you can still see her while you take care of your business. This could be a chair in the corner of the kitchen, or her high chair, or even a pillow that you move from room to room with you. Make sure that she knows that this spot is for time out and don't be afraid to use it. The guidelines that are recommended are 1 minute for every year of age. Now, if you put your baby in time out and she cries for that whole minute, she is learning that she gets what she wants (out of the spot) when she cries long enough. What I ended up doing with my daughter was that she had to sit until she got quiet and the second the crying stopped, I let her up. Believe it or not, it only took her 2 days to learn that if she was quiet, she got out of time out faster.
You stated that, "Ignoring her seems to make her even more angry." That makes it sound to me like she is doing all of this to get attention. My oldest used this type of ploy whenever she wanted attention and it made life miserable for me and the rest of my family. I can remember calling her father at work and telling him he needed to come home and get her because I could not take it anymore...she had been throwing a temper tantrum for over 3 hours because I would not let her have cookies until she ate her dinner. It is difficult as a parent to have to be in that situation because we want our children to have what it is that they want but at the same time, we want to do what is right for them and these two things don't always match up.
If your baby is crying to get attention the best thing you can do for her is to ignore her negative behavior. I have had to do this in the day care and it does seem to work pretty quickly as compared to scolding or discipline.