Fishback attended Austin-East High School, where he earned All-state honors in both football and baseball. He initially played out of position as an undersized offensive guard. On the defensive side he played at linebacker and defensive end. He initially accepted a football scholarship from Johnson C. Smith University, but opted to leave after a week, when he came to a decision that the football program wasn't what he expected. He would end up transferring to Carson-Newman University, where he was converted into a strong safety, even though he never played the position before. He was named a starter mid-way through his freshman season. As a senior, he was the runner up in the NAIA's Player of the Year voting and was named Conference "Defensive Player of the Year". He took part in 4 consecutive NAIA Division I championship games from 1986 to 1989, winning the title in 1986, 1988 and 1989. He finished his college career with 293 tackles, 11 interceptions and a 21.6-yard average on 7 punt returns. In 2013, he was inducted into the Carson-Newman Athletic Hall of Fame. In 2016, he was inducted into the Knoxville Sports Hall of Fame.
On September 4, 1991, the Atlanta Falcons signed him to their practice squad. He was promoted to the active roster on November 16. He played in 14 games as a reserve defensive back, posting 5 defensive tackles, 24 special teams tackles, partially blocked a punt, returned a fumble for a touchdown and returned 3 kickoffs for 29 yards. He was named the Falcons "Special Teams Player of the Week" 6 times. He was selected as a Pro Bowl alternate at the end of the season. In the NFC Wild Card playoff game against the New Orleans Saints, with the score 27-20 and less than 2 minutes left in the fourth quarter, the Falcons cornerbackTim McKyer intercepted a pass that sealed the victory, but instead of falling down, he chose to make a risky lateral pass to teammate Deion Sanders, who after a sizeable run, made another dangerous lateral pass to Fishback, who returned the ball for an apparent touchdown, that would be overruled when proven that Sanders had done an illegal forward lateral, thus the play ended as a footnote.
New York Jets
On March 13, 1992, he signed in Plan B free agency with the New York Jets. He appeared in the first five games, collecting 4 special teams tackles. He was cut on October 20.
Atlanta Falcons (second stint)
On November 3, 1992, he signed as a free agent with the Atlanta Falcons. He appeared in the final 7 games, making 7 defensive tackles and 8 special teams tackles. On August 23, 1993, he was placed on the injured reserve list with a sprained neck. He was released on October 4.
Dallas Cowboys
On October 13, 1993, he signed as a free agent with the Dallas Cowboys. He played mainly on special teams and registered 12 special teams tackles. He suffered a sprained right knee in the tenth game against the Phoenix Cardinals and was declared inactive for the next 5 contests. He was a part of the Super Bowl XXVIII Championship team. In 1994, he registered 17 special teams tackles. He was released on November 30.
