I thought she WAS in the Academy but ended up leaving...

Edit: Yep, according to Memory Alpha:

Beginning in 2366, Torres attended Starfleet Academy, where she participated on the Academy decathlon team. She later admitted that after quitting "The track and field coach was furious with me" (VOY: "Basics, Part II")

She also had to dodge several punches in the lab, which Chakotay later joked about, saying, "Only you, B'Elanna, could start a brawl in Astrotheory 101." (VOY: "Future's End, Part II")

Interstellar history was, according to Torres, "the one subject I almost failed at the Academy." (VOY: "Year of Heck")

Also among her Academy training was EV suit simulations. She thought "they felt peaceful, like floating in the womb," but years later, in actual practice, she said she felt "a little sick to [her] stomach." (VOY: "Day of Honor")

During her time at the Academy, B'Elanna dated Maxwell Burke; however, their relationship did not last long. (VOY: "Equinox")

Ultimately, B'Elanna had a hard time fitting in, often getting into trouble with instructors and faculty. Within two years at the Academy, she was suspended once and had four disciplinary hearings against her. Even though quite a brilliant student and promising engineer, she eventually dropped out of the Academy in 2368, at the age of nineteen. (VOY: "Caretaker", "Eye of the Needle", "Parallax", "Extreme Risk")

One of Torres' teachers at the Academy was Commander Zakarian, who taught Survival Strategies (VOY: "Caretaker"); another was Professor Chapman. Torres and Chapman argued constantly; she even later admitted that "I was always questioning his, his methods, his assumptions, and he was always slapping me down like some upstart kid." She was later surprised to learn that Chapman thought she was one of the most promising students he had ever taught and was disappointed when she dropped out. He had placed a note in her permanent record saying he would support her if she ever reapplied. (VOY: "Parallax")