A native of Terre Haute, Indiana, Cottom attended Wiley High School and earned four varsity letters playing for the basketball team.

He led the Red Streaks to 3 IHSAA Sectionals and 1 Regionals, reaching the state semi-finals in 1931[1][2] His HS teammate, John Miklozek would become a star at Indiana State University.

Cottom played college basketball at Purdue University under Piggy Lambert.

He played on the varsity team for three seasons, and as a junior in 1933–34, Cottom led the Western Conference in scoring.

He was named a consensus NCAA All-American at the end of the season.