Carey was selected to make his international debut at the 1980 Summer Olympics in Moscow, but had to withdraw when the United States boycotted the Olympics at Jimmy Carter's insistence due to the Soviet Union's invasion of Afghanistan. In 1981 Carey was the American champion in both the 100-meter and 200-meter backstroke, setting a national record in the latter, after moving to the University of Texas at Austin to train under coach Eddie Reese. In 1982 he collected gold in the 200-meter backstroke and 4×100-meter medley relay, and silver in the 100-meter backstroke at the World Championships in Guayaguil, Ecuador.