After the Olympics, Stockwell attended the University of Florida in Gainesville, Florida, United States, where he swam for the Florida Gators swimming and diving team under coach Randy Reese during the 1984–85 school year. He won three Southeastern Conference titles (50- and 100-yard freestyle, 400-yard freestyle relay), and received All-American honours in each of the three events. While attending the university he dated his future wife, fellow Gators swimmer Tracy Caulkins, whom he had met in the warm-up pool at the 1984 Olympics.