Can anyone give advice on a screaming baby 16 months?

Has she reached terrible twos early? She is screaming all the time. If she wants something, if she dosn't want something, if I stop her mid escape at baby groups, if she is bored, if she is angry,hungry,lonley,happy,sad etc. It is embarresing at baby groups when she screams if I pick her up or take something from her. She looks like a spoilt brat which I am trying very hard to make sure she isn't. I have tried to ignore the screams, tell her off for screaming and even giving her hand a tap to show it is naughty? What else is there??? I am getting to the end of my tether and would like to know what to do to stop her or if she will stop on her own. Thanks,