My daughter was really bad at this, too, probably right around the same age. Somehow she's getting the reaction she wants, even if you are trying really hard to ignore her.
The best thing to do is firmly tell her "no", as soon as she starts screaming, and give her a warning: ("if you scream like that, I'm going to put you in your bed...time out...crib....corner, etc., until you're done screaming"). The next time she screams, do exactly what you said you'd do, and walk away. She doesn't come out until she's done screaming.
Give her absolutely no attention, no talking to her, no more warning her, etc. If she leaves her time out spot before she finishes screaming, calmly, and without talking to her, return her to time out.
She is really more than capable of understanding exactly what you've told her, she just can't quite talk back yet. Believe me, it may take a week to break her of the habit, but if you don't break the habit, she'll end up like my niece, and scream at everything...even when she's a teenager! UGH!
Good luck! I think all moms go through it with their girls, just depends on how you deal with it NOW that will determine how they conduct themselves when they're older.
S.