I don't really know about that but I know toothpaste is good if you put it on them, it will suck the stuff out of them.
Prevention is the best thing though for long term clear skin. Pimples build under the skin for two weeks before they actually appear, which means that before any major event where you want clear skin you have to start washing your face two weeks before.
You should also wash your pillowcase every two weeks to keep the oil off it and if you are female tie your hair back because that will get oil on your face.
I hope this helps.