After graduation from high school, Charles attended Amherst College in Massaschusetts on a scholarship. He was named an all-American halfback and won the Thomas W. Ashley Memorial Trophy as the Most Valuable Player on Amherst's football team. He graduated in 1926 and received the Howard Hill Mossman trophy for his outstanding contributions to Amherst sports. After college, he became Director of Athletics and biology instructor at Morgan State University in Baltimore, Maryland. He worked at Morgan State for two years and led the football and basketball teams to championship levels.
Drew was always interested in science and wanted to pursue a medical career. He attended medical school at McGill University in Montreal, Canada. He participated in sports while in medical school and won many championships. He was captain of the track team and won the all-time top score at McGill in intercollegiate track competition.
One of Drew's instructors in anatomy was John Beattie a British doctor. Beattie was stydiying the techniques and problems of blood transfusion. Patients often died from a loss of blood after accidents or surgery before the 1930's and researchers were investigating ways to replace the lost blood through transfusions. Although Dr. Karl Landstiner had discovered the four different blood types, and found that the body would not reject a donor with the same blood type, the problem of finding a compatible donor in an emergency was unsolved. Drew was interested in solving that problem.