Greeson has been a member of her high school's varsity track team for five seasons and was captain for the last two seasons. She was a member of the varsity cross country team for four seasons and was captain during her senior year. She also lettered in soccer her freshman year. When Greeson was a freshman, she was awarded the Three-Sport Varsity Letterman Athlete of the Year in her school. She and her team qualified to run in the Florida State Championship cross country meet three years in a row. She was awarded the Cross Country Coach's Award her freshman and senior years. Greeson was also a member of the All-Conference team for track from 2009-1012. She also qualified for the Florida Track and Field State Championship for the 800-meter run and 4x800-meter relay from 2008-2012. Her best times are 19:58 in the 5K and 2:22 in the 800.
Greeson was a member of National Honor Society and was also named an AP Scholar. She graduated with High Honors in the International Baccalaureate Program.