Swaim attended Pleasant Valley High School , where he played linebacker and received All-section and All-league honors as a senior, after registering 124 tackles (65 solo), 6 sacks, one interception, one fumble recovery and 2 blocked extra points. He also practiced basketball .
After his sophomore season, he transferred to the University of Texas where he was a two-year starter, being used mostly as a blocking tight end and on special teams . He finished with 26 games (22 starts), 13 receptions for 84 yards and one touchdown .
Swaim was selected by the Dallas Cowboys in the seventh round (246th overall) of the 2015 NFL Draft ,  when the team surprisingly traded a 2016 sixth-round draft choice (#178- D.J. White ) to the San Francisco 49ers to assure obtaining his rights, after he was considering signing with the San Diego Chargers as an undrafted free agent .  He played well enough in the preseason to force the team to keep four tight ends .
As a rookie, he was declared inactive for 12 games, while playing in 4 contests. He had one start against the New England Patriots , when he replaced an injured James Hanna and the Cowboys opened in a three-tight end set. The season-ending injury to Gavin Escobar , gave him a chance to play in the last 2 games and record one reception for no yards.
Swaim was placed on injured reserve on November 16, 2016 with a pectoral tear.