Most of the medicines out there for headaches contain a great deal of caffeine, which is usually what stops the pain, if it really exists.
Caffeine regulates the blood vessels to stop the pounding effect.
The cold rag helps probably more psychologically than physically, calming the person down to let them relax and let their body fix itself. Soak in a hot tub of water with the cold pack on your head. An old remedy for stomach upset was a medicinal coal syrup. Soda without the bubbles helps if there is regurgitation. A piece of bread helps if there is excess mouth salivation from an upset stomach.