During his senior season, he was instrumental in the Aggies' first share of a regular-season Southeastern Conference (SEC) championship, as well as their run to the Sweet Sixteen in the 2016 NCAA tournament.

As a junior, he averaged 13.9 points, 5.4 rebounds, 1.5 steals, 1.1 blocks and 1.3 assists per game and was named All-District 23-5A First-Team honoree.

In the first round of the College Basketball Invitational, House hit the game-winning shot against Texas with 17 seconds left.

For the first three games of the season, House scored a total of 50 points in wins over USC Upstate, Southeastern Louisiana, and Texas A&M-Corpus Christi.

House would play for the squad throughout the month of November and the beginning of December, averaging 17.7 points, 6.3 rebounds, and 2.5 assists per game there.

Throughout the rest of the season, House would split his playing time there between Phoenix and their NBA G League squad, the Northern Arizona Suns.

House would make his debut with the team a day later, scoring two points and recording a single rebound in 11 minutes of play in a close loss against the San Antonio Spurs.

[13] House was later assigned to the Northern Arizona Suns affiliate alongside Davon Reed on December 28, mainly for healing purposes.

House then returned to action on January 5, 2018, recording what was at the time a new season-high 9 points in a loss against the San Antonio Spurs.

On February 23, his two-way contract expired, meaning he couldn't be allowed to play for Phoenix again until after the NBA G League's first season under its rebranded name concluded.

On April 1, House would record a new season-high with 16 points scored alongside 6 rebounds and 3 assists in a 117–107 loss against the Golden State Warriors.

[15] On June 26, 2018, it was revealed that House would play for the Houston Rockets in the 2018 NBA Summer League, in which he started in all five games.

[20] On January 16, he was sent back to Rio Grande after House turned down Houston's contract offers, both of which revolved around signing a three-year deal.

[16] On March 15, Chris Paul was rested against the Phoenix Suns,[citation needed] allowing House to join the starting lineup in his first game back.

[25][26] On September 11, 2020, it was announced that House had been expelled from the NBA's bubble in Orlando for violating the league's COVID-19 safety guidelines.

[27] House, who had missed two games while the league's investigation was pending, had reportedly had an unauthorized female guest in his hotel room for a span of "multiple hours.