Stockwell is a Queensland native who specialised in freestyle sprint events, and had a successful international swimming career during the mid-1980s including the Olympics, Pan Pacific Championships, and Commonwealth Games.

[7][9] Stockwell, along with teammates Greg Fasala, Neil Brooks, and Michael Delany, won another silver medal in the men's 4×100-metre freestyle relay, finishing in 3:19.68 – just 0.63 of a second behind the Americans' new world record of 3:19.05.

[11] He also teamed up with Mark Kerry (backstroke), Peter Evans (breaststroke), and Glenn Buchanan (butterfly), swimming the freestyle anchor leg to win the bronze medal in the 4×100-metre medley relay (3:43.25) behind the Americans (3:39.30) and Canadians (3:43.25).

[15] 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.

He claimed a gold medal with his Australian teammates Fasala, Matthew Renshaw, and Neil Brooks in the 4×100-metre relay (3:21.58), and finished seventh in the 100-metre freestyle (51.61).

[19] Stockwell married American swimmer Tracy Caulkins, a three-time Olympic gold medallist, in 1991 in her hometown of Nashville, Tennessee.

[23] Stockwell ran in the election for the presidency of the Australian Olympic Committee, in the race to succeed John Coates in April 2022, but lost to Ian Chesterman.

During the 2019 Australian federal election campaign, Stockwell made a donation of $1,200 AUD to the Liberal National Party of Queensland (LNP).