Yes, she may scream herself hoarse or give her self a head rush from shaking her head so hard... BUT there is NO reason to give in to her temper tantrum. She needs to learn self control and self discipline. The only way for her to do that is for YOU to guide her in those paths. Let her scream till her voice cracks. BUT DO NOT YELL BACK!
Be prepared. You have a fight brewing. It will take patience and consistency to stop this. You will have to be tough. But the alternative is having a child who rules YOU and shows her younger sister how to do it also. Do you want 2 kids screaming at you?
No means NO! Do not say it more than 2 times. Do not yell it back. Calmly say no and give her the reason (close to dinner, not enough time, nap time, mommys tired, etc)If she continues, say no again and then comes punishment. If you are in a public place, pick her up and carry her to a quiet place for it, or leave. DO not give in at all. I have had my kids stand with their noses on the bathroom wall at times. Even my 2 yr old will put himself in the corner if he knows he's done something worthy of punishment.
You may want to avoid going out until the training at home is being comprehended by her.Start by sitting down with her and telling her that the screaming is not allowed. The temper tantrums are not allowed. When mommy says NO it means no! Make sure that anyone else around your kids follows this also. Their no means no...
When she does melt down punish her (not sure what your stance is on spanking, but in this situation spanking WILL make it worse)by time out. Time out means NO interaction. Put her in a chair somewhere she can not see a tv that is on, no toys, not in her room. you sit across the room. Do not look at her or speak to her. QUIET! Get a book and look at it. Act like she's invisible. Let her scream if she wants... But if she gets up walk over tell her calmly "Its time out. You have to sit here for 3 minutes. Calm down. We do not act this way. Mommy said NO" Say this everytime. It explaines to her WHAT you are expecting and WHY she is in trouble. Then put her back in the chair and start the timer over.
I have had some pretty bad kids that got the idea in one day and others that it takes longer to get them to understand time outs. (I do daycare and have 3 of my own)
Once she understands the idea of a timeout chair it will be easier to insist on behaviour in public. But do not threaten unless YOU will follow thru. If in a store and she needs a time out push your cart to customer service, tell them you need to go out to your car for a bit. Take the kids and go out in the car. Have the time out in the car. Not only does this get what ever shes screaming about out of sight... But it lets her know You are serious. If she does not calm down move the car to the farthest end of the parking lot and let her scream it out or go home and try shopping again later when she is calm and agrees to listen.
Keep track of WHEN she is having melt downs. Is it afternoon? She may need to still have a quiet time/ nap.
The roads you pave when they are young make life a lot easier when they are older!!! As motivation to stick to it, If your worried about this when she is 3, think of how she will be at 12/ 13 and she knows swear words and how to be purposely mean and disobedient.
There are lots of moms out there trying to do the same thing. Its called raising a respectful child. YOU can do this!