Hi R.,
My daughter is almost two now, and is going through a similar phase of becoming very angry/frustrated/loud! And it is SO embarrassing when we are in public, because you think that everyone is watching you and criticizing your parenting skills! Ack!
The first thing to remember is that she is still just a baby, and that this is normal and natural developmental phase. She can't think the way that we do, so she's not consciously thinking "I'm going to drive my mom crazy," but she's realized that this is a language that mom understands - it certainly gets your attention!
Primarily, your daughter wants to know two things - that she is heard, and that she is loved. The yelling is a new way for her to express her power, which she is just learning that she has. So it is very important that you respond CALMLY. Yelling or becoming angry only makes her understand that when she shouts, it gets your attention more intensely, which may be what she wants. Try to think of her as your best friend who is just so upset, that she doesn't know what to do. Talk to her with love and pity in your voice, so that she knows you love her.
First of all, try to keep an eye on her to notice her signs of frustration BEFORE she gets to the yelling stage. We've worked with our daughter to give her the language she wants - which is really what the yelling is all about - it's like your daughter wants to tell you some very important things, but doesn't have the words for it. So, at home, when she gets fussy and mad, get on her level and truly sympathize with her. Say, "Are you angry?" "Are you mad?" "Do you feel frustrated?" or a combination of those things. You'd be surprised how smart your little girl is and how quickly she'll catch on that you're on her side, and that you do love her. It's very important that you say this lovingly, because she can tell when you're fibbing. And pretty soon, instead of yelling, she'll be able to tell you "are you angry! (baby translation: I am angry!)" to tell you how she feels!
Secondly, make certain that when you do get angry (and we all have those times!), that you are able to talk with her about it, after you calm down. You can say things like "Mommy was SO mad!" "I felt grumpy!" "I felt angry like a dinosaur/bear/lion!" and then you can make the animal sound and invite her to join in - making her understand that EVERYONE gets angry at times, but it's okay, and we feel better afterwards. She needs to know that her anger is a real feeling, and that she is still a good person, even though she feels that way sometime - and it's good for you to know that, too!
And, if it ever gets to the point where you do end up yelling or shouting or getting out of control (try really hard not to grab or push or become physically fierce), it is important that you apologize. You can say "I'm so sorry that I yelled. I was so angry! Did you feel sad when I was yelling?" and once you've done that, make some play time out of it. Say "Was it loud? Can you be loud with me?" If you give both of you time to play with being loud, then yelling becomes less emotionally-charged.
But, above all, know that this is a phase, and that it will pass. You may miss it during the battle of wills when your daughter is 15 (people tell me that all the time, but I still can't believe it). Our daughters are great tests to us, and they help us grow in ways we never could have without them.
And, most importantly, know that you are doing a GREAT job as a mother, which is the hardest and most important job in the world. Good work (and good luck)!
Warmly,
~L.