D..
GrammaRocks is spot on. Do what she says every single solitary time. Even 10 times in a row if you have to.
She found out that screaming works. Why WOULDN'T she continue if she gets what she wants? And by the way, giving her attention (yes, negative attention is still attention) is something she wants. If she can still be with you and arguing the point with you about what she wants, she has more of a chance of wearing you down to get what she wants. Thus, she continues to scream and have fits.
Make sense? Put her in her room and don't let her come out until she isn't screaming anymore. (Don't let her know you are out in the hall holding the door... she must think that she does not have an audience.) Then do exactly what Gramma is telling you to do...
Dawn