P.W.
Yes, get down on eye level and look her straight in the eye. Very softly tell her that when she speaks in a soft voice like you are speaking right now that your ears will be able to hear her better. Don't respond to any loud requests without doing this and getting her to lower her voice.
My guess is when she screams just to scream she is testing the sound of her voice. You can do the same as above, but instead of telling her it is not okay, tell her that it hurts your ears and to please use a voice that is soft like the one you are using now, or put her in her room and close the door. Tell her she can scream when she is alone and it doesn't hurt others ears.
Then the old inside and outside voice thing.