I think I'd be inclined to not give her attention for that behaviour. You can redirect her, which will of course make her shriek, tell her (in very firm voice) 'NO thank you! We do not scream!", then leave her. She will likely keep screaming or maybe cry, but may make the connection after a while that the screaming isn't getting her any attention at all. I wouldn't doubt she's enjoying the attention she gets. When she stops screaming, then approach her.

Another approach might be to put her in time out to help her make the connection. I've had screamers too, and those are the approaches I used. I worked after a while.

Screaming = time out = no fun at all