I asked my girlfriend to not drink alcohol at all at a new years party I can't attend myself
It sounds like you don't want your girlfriend to enjoy herself if you can't go to the party.
I don't want her to embarrass me, that's why.
How would she embarrass you? If she's going to a party, she deserves to have a good time. Trust your girlfriend to make good choices, I'm sure she will.
She has no self control and will act like a fool at the party since I'm not there to keep her under control.
I think it's unfair for you to limit her behavior at a party that you can't attend. Her behavior won't embarrass you and you have to trust her and let her enjoy herself. Trying to control her will really upset her.