Welcome to tantrums!!! Isn't it great! Lol! First, the best thing you can do is keep your sense of humor, if you watch them, it's quite funny.
The next thing is DO NOT try to appease them. They can't be reasoned with at that time anyway. What I used to do with my oldest daughter when she'd scream, which was quite often BTW, was just put her in her room. I told her that I was sorry she was so upset and if she wanted to scream, that was fine but Mommy would NOT listen to her. They are tiny people with BIG emotions and they just get overwhelmed by them sometimes.
The main thing for you is too stay calm and DO NOT give in to her tantrums. Your daughter needs to see that screaming and throwing a fit will NOT get her what see wants. You must also tell her that her behavior is not acceptable.
Be prepared that this will only get worse before it gets better. 3's are worse that 2's in my experience!! My child finally started calming down around 4 1/2. My son, my first was like yours. He NEVER had full blown tantrums. Then my daughter Kaylie came along and all hell broke loose. My 3rd child, Eden is also a girl and just turned 2 so we are starting tantrums. However, she's nothing compared to her sister!!! Lol! I tell her that too!
Hang in there, Mom! You too will weather your daughter's storms.
God bless!
Chris