Barrow attended John Ehret High School in Marrero, Louisiana, where he played on the Patriots football team. He was named District 8-5A Defensive MVP and Louisiana Class 5A All-State as a senior. He recorded 71 tackles, 13 tackles for loss, nine quarterback hurries, two interceptions, five forced fumbles, and four fumbles recovered with two of those returned for touchdowns.
Considered a three-star recruit by the Rivals.com recruiting network, Barrow was rated as the 22nd best inside linebacker prospect of his class.
Barrow attended Louisiana State University where he played for the LSU Tigers football team from 2009 to 2013 under head coach Les Miles. During his collegiate career, he appeared in 51 games, including 28 starts, where he accumulated 230 tackles, including 14.5 for loss, 1.5 sacks, seven pass break-ups, one forced fumble, and four fumble recoveries. As a redshirt senior, he was named a second-team All-SEC selection.
Barrow was drafted by the Denver Broncos in the fifth round (156th overall) of the 2014 NFL Draft.
In 2014, Barrow played in all 16 games with one start in his rookie season with the Denver Broncos. On September 5, 2015, Barrow was waived.
Barrow was signed to the Chicago Bears' practice squad on September 7, 2015. On September 12, 2015, he was elevated to the active roster after Sam Acho's release.
Barrow was placed on injured reserve on August 31, 2016 after suffering a foot injury in the third preseason game. He was released by the Bears on December 5, 2016.
On December 28, 2016, Barrow was signed to the Dolphins' practice squad. He signed a reserve/future contract with the Dolphins on January 10, 2017.
On July 30, 2017, Barrow was waived/injured by the Dolphins and placed on injured reserve.