[4] His elder sisters attended Hamilton High School in Chandler, Arizona, where Shough and his younger brother Brady played in the football program.

[5] Shough became the starting varsity quarterback as a junior at the high-profile Hamilton High School football program in the 2016 season.

As a senior, Shough played for Hamilton in its 2017 season when allegations of hazing were publicized, which resulted in the conviction of three players and the permanent reassignment of three administrators, including head coach Steve Belles, to Chandler Unified School District (CUSD) offices.

[15] Multiple athletic scholarships were offered from Alabama, California, Georgia, Florida State, Michigan, South Carolina, and Indiana.

[16] After an initial verbal commitment to North Carolina in June 2017,[17] Shough signed an early letter of intent to Oregon in December 2018.

[23][24] Going into 2020, Oregon head coach Mario Cristobal indicated early that Shough would be the starting quarterback (vacated by Justin Herbert being moved to the National Football League (NFL)).

[22] Oregon and the other Pac-12 conference member schools began play in November with strict policies regarding testing, positivity rate, and contact tracing for the COVID-19 pandemic.

[26][27] Despite Shough starting the Pac-12 Championship Game against USC, Boston College transfer Anthony Brown began to take offensive series.

[28] Oregon was selected to the Fiesta Bowl held in Glendale, Arizona, which is inside the Phoenix Metropolitan Area where Shough grew up.

Arriving at Texas Tech, Shough battled for the starting quarterback position against senior Henry Colombi and freshmen Maverick McIvor, Donovan Smith, and Behren Morton.

Notable individual performances include a four-touchdown, 342 yards-passing showing in a 52-45 loss to the University of Miami (FL) at home, as well as playing a major role in the 33-21 upset win vs Clemson on the road.

[50] On December 17, 2024, Shough was among three winners for Comeback Player of the Year awarded by the College Sports Communicators (CSC) organization alongside Utah State DB Ike Larsen and South Carolina RB Raheim Sanders.