Career
Karlström started out his career playing for Hammarby Fotboll at the age of six. When he turned nine the coach of his team moved to IF Brommapojkarna and brought his entire youth team along with him to the new club, including Karlström. Shortly after his eighteenth birthday in 2013, Karlström made his Allsvenskan debut for Brommapojkarna away against Kalmar FF. At the start of the next year he scored for the first time when his game-winning goal in the last game of the 2013-2014 Svenska Cupen group stage qualified the club for the knockout stage of the tournament.
Brommapojkarna were relegated at the end of the 2014 Allsvenskan season, but Karlström had performed well enough to be signed by the larger Stockholm club Djurgårdens IF on a four-year deal.
Karlström has represented Sweden at the U17, U19 and U20 levels. In November 2014 he made his debut for the Sweden national under-21 football team against Austria.