Sherwood was introduced to hockey with his brother Kiefer by their father Roger. After playing in 31 games for the Ohio Blue Jackets U18 team, Sherwood played three games with the Youngstown Phantoms in the United States Hockey League during the 2014–15 season. On February 9, 2015, Sherwood committed to play NCAA hockey for Boston University. While Sherwood and his brother went undrafted to the NHL, they were both invited to the Columbus Blue Jackets 2015 development camp. He eventually signed an entry level contract with the Blue Jackets on July 17, 2015, forgoing his NCAA eligibility. Instead of joining the Boston Terriers, Sherwood committed to the London Knights of the Ontario Hockey League for the 2015–16 season. On September 29, 2016, after playing his rookie season with the Knights, Sherwood was traded to the Flint Firebirds in exchange for two second round picks and one conditional pick. After having a career-high season with Flint in which he recorded 85 points in 60 games, Sherwood was traded to the Kitchener Rangers in exchange for draft picks ranging from 2019 to 2021. While with the Firebirds, Sherwood made his professional debut with the Cleveland Monsters, the Blue Jackets American Hockey League affiliate, in April. Sherwood was returned to the OHL for the 2017–18 season where he completed his major junior career with the Rangers. After attending the Blue Jackets training camp prior to the 2018–19 season, he was assigned to their AHL affiliate, the Cleveland Monsters, to begin the season. On November 21, 2018, after playing in eight AHL games, Sherwood was assigned to the Monsters ECHL affiliate, the Jacksonville Icemen. The demotion was short-lived as he was recalled back to the AHL on November 26, after playing in three games. He was recalled to the NHL on January 13, 2019, after playing in 22 games for the Monsters. Although he was sent down without making his NHL debut, he was recalled again in February. Sherwood eventually made his NHL debut on February 16, 2019, against the Chicago Blackhawks, becoming the first player from central Ohio to play for the Blue Jackets. In his debut, he played 6:58 minutes alongside Riley Nash, Lukáš Sedlák, and Anthony Duclair to help the Blue Jackets win 5–2. He was reassigned to the Monsters on February 19 after Brandon Dubinsky was activated from injured reserve. Sherwood attended the Blue Jackets training camp but failed to make their opening night roster. After spending the beginning of the season with the Monsters, Sherwood was called up on November 3, 2019. That night, Sherwood was roughed by Calgary Flames forward Milan Lucic who was subsequently suspended for two games.
