If you use regular toothpaste to get rid of the hickey you'll also need to apply some peppermint oil to the hickey before applying the toothpaste to the hickey.
You can also use peppermint based toothpaste to remove the hickey without using peppermint oil.
Toothpaste does get rid of hickeys if you do it the right way.
Rub the toothpaste over the hickey and leave the toothpaste on the hickey for several minutes until the tingling feeling stops.
Then just wash the toothpaste off with a washcloth.