We've been dealing with this for about a year and try lots of things from ignoring to explaining to whispering, etc. It's been getting better, but it's still hard. She doesn't scream in the car anymore, which is good, b/c I think I was blacking out and missing turns, etc. Scarry!
A thing we are trying is consequences. Espec if it happens in a public place:
e.g. At teh market: "We will leave and go outside until you can get yourself together and talk in your inside voice, then we will come back."
You can't just leave, b/c then they think screaming will let them control the situation, so you focus instead on them controlling themselves and getting them to understand they WILL go back to the market, restaurant, etc.
But you need to be prepared for your meal to get cold, or shopping to take longer, etc.
Conversely, you also need to know when the babe will and won't be able to handle a dinner out or a trip to the market. Dinners out may have to be put on hold awhile, KWIM? I try to pay extra attention to how tired she is, etc, before we run any errands etc.
1 yrs old seems kind of early maybe for the suggestion I am making. Our DD is 2 now and she's just getting it. Doens't always work, either. But it was reco'd to us from a child educator and we're trying it mostly b/c we've been at a loss.