OK, this is a bit time consuming, but if pick a couple days to work on it, it will nip this problem in the bud.
I also have an outgoing (read loud), strong-willed daughter (2 1/2 now, but this problem hit right about 2). I followed John Rosemond's advise in his book "How to make the Terrible Two's Terrific" and that was to make it as much of a non-issue as possible.
Before we went into the store, I would tell my daughter that if she screamed inside (she would squeal when she got restless) we would go to time-out in the car. You have to do this on a day when you're prepared (ie. probably don't have your other child) and you've parked the car close by! Of course, Anna squealed within a couple minutes and I whisked her out of the store, leaving the cart where it was, walked calmly to the car, plunked her in her carseat, buckled her in and sat her there for a minute or so just calmly saying, "this is time-out for squealing in the store, we don't do that." Then I took her out, brought her back to the cart and resumed shopping. Of course she screamed again within minutes - it probably happened 3-4 times that first day, but she got the point: her squealing was NOT going to shorten the shopping, it was just getting her time-out. The next time or two that we were at the store, she squealed 1-2 times, but after that, she dropped it completely. Now, whenever she starts to misbehave in public, I just tell her, "settle down or we'll go to time-out in the car" - and since there is no point or fun in that, she settles down and that's that.
I agree with other posts that say don't let your kid cry it out at the expense of others. I used to let her scream, thinking it would go away with no attention. But of course it just got worse. AND, it's a public place for goodness sakes. I don't know what I was thinking. We should actively teach our children what is appropriate behavior. By ignoring her, I was OK'ing her screaming. Removing her from the store let her know that a store is a special place and certain behaviors are simply not tolerated by others. Try this - trust me, I've got the upper-hand now.