Tomori started to play handball at the age of 12 and signed her first professional contract with Vasas SC in 2004. Considered one of the best players of her position in the Nemzeti Bajnokság I, she moved to league champions Győri ETO KC in 2007. After spent two successful seasons at the club, winning the league and finishing runner-up in the Champions League, in March 2010 dressing room troubles were revealed. As a result, first the Hungarian international was exiled to the reserve team, and after the sides could not find an appropriate solution, she left the club by mutual agreement. As she told in an interview, several teams have traced her after she became a free agent, including Békéscsaba, Vác and other sides from abroad, but decided to join Ferencvárosi TC. She stated that the talks with FTC executives and their future plans had a great influence on her choice. She spent five seasons with them, when she got an offer from her former club Győri ETO and decided to grab the opportunity, therefore she signed a contract with them. After the agreement went public, she explained her choice as: "I signed for Győr, because I want to win Champions League." In March 2019 she decided not to extend her contract with Győr and signed a deal with Siófok. About her decision, she said: "Győr wanted to keep me, but they offered only a one-year contract, meanwhile Siófok gave me a 3-year offer, and this was decisive at the end because my goal is to have a secure and stable future."
Tomori got injured seriously for the first time in December 2015 at the World Championship during the match against Poland. The diagnosis was anterior cruciate ligament tear and a partial lateral ligament injury. She was out for eight months and returned to handball in autumn 2016. During a training in October she felt that her operated knee hurts, the doctors after an examination decided that one more surgery is needed. Tomori recovered from this surgery for January 2017. After the 2016–17 season another operation was needed, because of a cyst that has emerged at the location of the screw exception. She recovered in time and was able to start the preparations with her team, Győri ETO. In October 2017 during a 2018 EURO qualification match against Belarus she has suffered a knee cartilage injury, which required an arthroscopic procedure. Her recovery was successful, she could return to the court in January 2018. In March 2018, during a match against The Netherlands she twisted her other, "healthy" knee unluckily and suffered a rupture in her anterior cruciate ligament. Later she admitted, that after this injury she was thinking about retirement, but other athletes – like Anita Görbicz – convinced her, that she can still play on the highest level, even if both knees have been seriously injured before. She made her comeback in January 2019, after 9 months of successful rehabilitation.
