B.S.
This is so common! I don't think there is much to be done about it but be patient. You really can't discipline a 16 month old. She is just experimenting with her voice and with the power she has to affect people. Screaming gets a big reaction! Thats pretty cool - I think I'll scream some more! Look how crazy it makes all the adults! Yay!
Really, though, both my son and daughter screamed like this and it drove me mildly crazy and my husband positively nuts. He hated it. Honestly, though, they just outgrow it when they learn more words and more effective ways to communicate. In the meantime, try to give no response at all to screaming and to distract her as quickly as possible. She starts to scream - start singing a song, playing pattycake, asking how big she is, getting a new toy, whatever.
It will pass, I promise!
B.
Mom of two prior screamers