Toddler tantrums in public

I need help! I have a 2 1/2 year old. Obviously temper tantrums are normal and I expect her to tell me no and all that but here’s the thing.. its like nothing works for her.

For example, we are in a grocery store. She doesn’t like something, she will just SCREAM her head off, drop to the floor, fight you, kick, hit, etc.

If we are in a restaurant and she drops a spoon or decides that she doesn’t want to be there, same thing. Screams at the top of her lungs.

Today, we are at the doctors and my husband tried to grab her hand to walk with her so she isn’t running and she didn’t want to hold his hand. So she dropped to the ground and screamed no and the top of her lungs.

Every time she does this, we pick her up and take her out until she calms down. We tell her no, sometimes even smack her hand. We keep taking her out until she calms down but it doesn’t work! Today she had my phone and she threw it so I refused to give it back, as well as took her out and told her why I wasn’t giving it back. She lost her mind.

It’s like in public it’s 100X worse and she’s always been like this. It’s not new, but we’ve tried everything possible. At home, she goes into time out until she calms down then I explain what she did and we go from there but that just doesn’t work in public.

How do you deal with temper tantrums in public? We tried telling her that people were looking and think she’s a baby, she doesn’t care. We tried rewarding good behavior, doesn’t work.