Michał Rozmys first appeared in national competitions over the 800 meters in 2011. In 2012 he was Polish U18 indoor champion over 1000 meters in 2: 31.72 minutes. By 2014 he improved his time over 800 meters to 1: 53.73 min. Since 2015 he has also competed over the 1500 meters. In July he set his season best of 3: 50.16 minutes. Another year later, he improved his 800 meter time by almost four seconds, over 1500 meters by more than ten.
Due to his good performance, he entered the U23 European Championships in his Polish homeland in July 2017 , where he won the bronze medal over 1500 meters in 3: 49.30 minutes. In the same month he was then for the first time Polish champion over 800 meters. In August he competed in his two specialty disciplines at the World Championships in London. In both competitions he qualified for the respective semi-finals, where he failed over 800 meters just to make it into the final and took eleventh place there. Also in August, as a student at the University of Szczecin, he took part in the Universiade in Taipei, where he was just eliminated in the semi-finals over 800 meters. In 2018 Rozmys competed over 800 meters at the European Championships in Berlin. In the final he set a new best time of 1: 45.32 minutes, with which he finished in fourth place.
In spring 2019 he started at the European Indoor Championships in Glasgow, where he was eliminated in the preliminary stages. In July, he won the gold medal over 1500 meters in 3: 53.67 minutes in his second appearance at the Universiade in Naples . He won two more gold medals at the 2019 World Military Games in Wuhan.