When my daughter throws a tantrum in public, I firmly tell her to stop and most of the time she will but when she's extra tired and cranky, I make her sit directly where she's throwing her tantrum until she's calmed down. Whether it be on a sidewalk, on the floor, whatever, I just tell her to sit. It's the change of position and the fact that she's not allowed to get back up that makes her settle down. When that doesn't work even still, we do have time out. If you can't exactly give time out in the mall, carry her if you must but remove her from the situation. Just pick her up and walk away (this saves you the embarrassment and emotional drama as well because you can get away from all the people).

When I threw fits as a kid, my dad asked me "do you need to go to the bathroom?" which was code for 'if you don't stop, we're going to the bathroom and I'll whip you". I shut up quick most times.

when all else fails, I do Hug and Kiss therapy. When my daughter starts showing signs of agitation and I feel myself getting angry too, I grab her fast and hug her tight and kiss her face all over. It makes her laugh instead of freaking out and it settles me down as well. Tickle therapy works just as well.

Good luck to you.