Toothpaste does work for some people to get rid of the cold sore but some people have said it doesn't work.
It's worth a try though as the toothpaste is supposed to dry out the cold sore and help it heal faster.
You can also apply a cold compress to the cold sore or some baking soda paste to the cold sore.
Cooling your cold sore with some ice cubes and/or applying some Visine can also help with the redness and healing of the cold sore.