How do I handle my 3-year-old's constant defiant screaming?

My 3-year-old daughter has become increasingly difficult and defiant. I know its normal for a child of this age to become very frustrated in trying to show their independence, but her form of temper tantrums have become ALL day screaming "No!" over and over and over, as loud as she possibly can. Honestly someone could easily hear her screams a few houses down, I'm sure. I try putting her in time-outs for misbehaving and this just results in the ear-piercing, blood-curdling screaming the entire time. If I tell her to do something she doesn't want to do, or if I don't allow something she wants, I get the screaming-bloody-murder tantrums once again. I have tried for a while to ignore them, and nothing is changing. I have tried which does nothing but increase the screaming. Nothing has worked. I am at a loss as to how to discipline such a stubborn, defiant, and exceedingly out of control child. She does not behave this way at preschool luckily, just at home. Her behavior is so out of control that very often throughout the day my 15 month old daughter is very frightened by her and will cry a lot. She also pushes her sister if she gets angry, has been "hoarding" toys so that her sister can't pick up a toy and play with it, and there have been a few recent bites, and she has never been a biter before. I am just losing my mind and it's just getting worse all the time. How do I get her under control and get the screaming to stop???