An African-American and the youngest of seven children, Garrison started playing tennis at the age of 10 and entered her first tournament at the age of 12. Her success as a junior player quickly made the tennis world take notice. At the age of 14 she won the national girls' 18s title. And then in 1981, she won both the Wimbledon and US Open junior titles and was ranked the World No. 1 junior player. Garrison graduated from Sterling High School in Houston in 1982. In 1992, Garrison finished runner-up in the Australian Open women's doubles (partnering Mary Joe Fernandez).