There is really no reason for individuals to donate medicine or medical supplies to a disaster relief effort. And under no circumstances should you donate opened or unused medications from your personal supply, particularly prescription drugs. Not only is it a waste -- they will need to be thrown away -- but they could pose a danger to those handling the drugs.
Disaster relief agencies and first responder units are usually well-stocked with the provisions to manage a medical crisis. When there is a need, they will work directly with drug companies and medical suppliers get the right supplies to the right place.
A 1999 report from the World Health Organization issued guidelines for medical donations to disaster areas and war-torn regions. Among the common problems it saw were poorly labeled packaging, expired medications and drugs sent that had nothing to do with the medical problems on the ground. After a 1988 earthquake in Armenia, the country received 5,000 tons of drugs and medical supplies worth $55 million. It took a staff of 50 people six months just to catalogue the donations, most of which were only labeled with brand names; less than half were useful for emergency medical needs. During the war for independence in Eritrea in 1989, seven truckloads of expired aspirin were donated, which took six months to burn [source: WHO].