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 catalog the donations, most of which were only labeled with brand names; less than half were useful for emergency medical needs.