She played college basketball for Louisiana Tech, where she helped lead the Lady Techsters to national championships in 1981 and 1982. While only a sophomore in 1982, she was the leading scorer in the NCAA tournament, and was named the tournament MVP.
Braxton was a member of the 1983 Pan American team that won a gold medal in Venezuela.
Braxton was a member of the USA National team at the 1983 World Championships, held in Sao Paulo, Brazil. The team won six games, but lost two against the Soviet Union. In an opening round game, the USA team had a nine point lead at halftime, but the Soviets came back to take the lead, and a final shot by the USA failed to drop,leaving the USSR team with a one point victory 85–84. The USA team won their next four games, setting up the gold medal game against USSR. This game was also close, and was tied at 82 points each with six seconds to go in the game. The Soviets Elena Chausova received the inbounds pass and hit the game winning shot in the final seconds, giving the USSR team the gold medal with a score of 84–82. The USA team earned the silver medal. Braxton averaged 8.9 points per game.
In 1984, the USA sent its National team to the 1984 William Jones Cup competition in Taipei, Taiwan, for pre-Olympic practice. The team easily beat each of the eight teams they played, winning by an average of just under 50 points per game. Braxton averaged 6.7 points per game. 
She won a gold medal with the USA Women's Olympic basketball team in 1984.
Braxton played 13 seasons in Europe with Vicenza, Messina and Parma in Italian League. The Vicenza team won four European Champions Cup while Braxton played for the team, scoring almost 23 points per game. She earned All-Star honors in 1997.