Burrows made into the international scene, when he represented his homeland Bahamas at the 2008 Summer Olympics in Beijing. He competed for the men's 50 m freestyle, and swam against contenders, including Switzerland's Flori Lang and Lithuania's Rolandas Gimbutis, in the eighth heat of the competition. Burrows completed his event, with a time of 23.19 seconds, finishing seventh in the heats, but placing fifty-second in the overall standings. Despite his disappointing result at the Olympics, Burrows eventually emerged as one of Bahamas' most prominent swimmers in the late 2000s. At the 2009 FINA World Championships in Rome, Italy, he had set four national records in the men's sprint freestyle and butterfly events, which were all previously held by former Olympic swimmer Allan Murray. He also competed at the 2010 Central American and Caribbean Games in Mayagüez, Puerto Rico, and won a bronze medal in the men's 50 m butterfly event, with an impressive time of 24.30 seconds.