Fellow boozehounds write in and set the record straight. I am both a bartender and someone who is well experienced in both biology and the effects of alcohol. Typically a hangover is simple dehydration.
Alcohol prevents the body from absorbing the necessary water to keep itself functioning.
It is simply too preoccupied forcing the liver to detoxify the blood to devote any time to water absorption. When the body becomes dehydrated the brain actually swells causing immense pressure inside the skull, thus the headache. Therefore, the best cure for a hangover is to drink as much water as physically possibly before going to bed. Taking bitters with 7-Up or Ginger Ale does work, but only because it is more alcohol. Your recommendations of taking Advil are very dangerous.