I have a little girl that screams/temper tantrums as well. She is also 2 y.o. I find when I don't make an effort to balance the day between her needs and the rest of the family's that she has a meltdown. Meaning, I always have an errand or something related to the house that has to get done so try to make her involved and let her know that we will go to the park or the play area at the mall after, etc. I also try to provide her as many choices as possible. Even down to the kind of socks, etc.
When I make this effort, I find the temper tantrums abate. I think it has a lot to do with them trying to gain control so I give her control through constructive ways.
That may help, if you aren't already doing it.
I wish you the best as I know what it is like to be out in public and feel like "poo" as your kid is wheels off and looks like they are running the show.