I'm going through the same with my 18mth old DD, I hear you on being embarrasing when you're out, we just had one at the doctors, anyway....

When we're at home I put her somewhere safe like on carpet because she bangs her head on the floorboards, then I walk away. When she calms down she'll come back to me and I'll give her a cuddle and forgive and forget. Ignoring it works best for us, she will usually put her head up and notice no one is paying attention then she'll give up. I don't even try reasoning with her because I know she's not there yet. Good luck there's no easy answer, you just need to find a way to manage it the best you can!