Fjällström comes from Tärnaby and skied for the first time at the age of three. She celebrated victories in Swedish youth competitions and, after reaching the age limit, took part in FIS races for the first time in November 2010 , in which she achieved top positions from the start. Since 2011, Fjällström has also been competing in the Junior World Championships , where her best result so far is a 14th place in the 2012 Roccaraso slalom . After she failed to achieve a result at the European Youth Olympic Festival 2011 in Liberec due to two failures, she was more successful at the first Winter Youth Olympic Games in Innsbruck in 2012 : She won the gold medal in the super combined, was fifth in the giant slalom and sixth in the super -G. She was only eliminated in the slalom.
In the European Cup Fjällström start since the 2011/12 season . After several top 10 placements, she celebrated her first victory in the Vemdalen slalom on November 27, 2012, at the beginning of the 2012/13 season . A month earlier she had competed in the World Cup for the first time in the giant slalom in Sölden . At the Junior World Championship in 2013 , she won the gold medal in slalom. She got her first World Cup points on December 17, 2013 with 29th place in the Courchevel slalom . Her best World Cup result so far is 13th place in the slalom in Lienz at the end of 2013. During slalom training in Saas-Fee , Fjällström suffered a cruciate ligament rupture on her left knee on September 16, 2014 , after which she had to pause the entire 2014/15 season.
After a one-year break, Fjällström started again in the World Cup, but had to break off the 2015/16 season again after one month due to an injury. In the winter of 2016/17 she was used in the European Cup, where she was only twice in the top ten. Things went better in the 2017/18 European Cup season with one win and two more podium places.