Screaming

I am officially the mother of a 3 year old with only one level of volume- Screaming.
Not just any screaming, the blood curling, high pitched, eye wincing, want to rip your ears off kind of screaming.

I am feeling defeated. I have tried being sweet and soft spoken and help her understand the screaming hurts people's ears. Nothing seems to help. I know mostly it's just the age, but holy cow my ears can only take so much...not to mention in public I can only take so many eyes on me before I want to melt away and disappear.

Here is an example of life in my house lately:

Took Emmie's cup to fill with juice during dinner. She started SCREAMING. I tried to tell her I put juice in it and to try it... it took awhile to convince her to try it and she spit it out screaming it was yucky. I dumped it. She was still screaming, I had no idea if she wanted water or juice or what! After standing there, eyes wide, completely and udderly confused, I put the cup down and continued washing dishes. Randomly she calmed down and asked for juice and I filled it back up with the same juice and she happily drank it.
What the HECK?

It's like a little demon takes over my child at random times. I feel completely defenseless and lost in what to do, how to help her and how to discipline her.

Any advice is welcome....and mailing me ear plugs would be much appreciated :)