I burned my bathroom sink with boiling water! how should i fix it?

I was trying to unclog my bathroom sink with baking soda, vinegar, and boiling water. I fixed the clog in the bathroom but realized my bathroom sink was made from cheap white plastic material covering a marble like surface.
Now I have little burned holes in my bathroom sink. The sink is not leaking any water since it has some sort of a hard surface underneath the plastic material but my sink looks like a coral(cause of the holes). I was thinking maybe I should fix it by putting some waterproof plaster on it?
Good idea or bad? I know I should avoid draining the plaster down the sink but any advice will be appreciated.

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