Born in Barry, Vale of Glamorgan, Swallow attended Eglwys Newydd Primary School in Whitchurch, Cardiff from 1994 to 2001.
Swallow played schoolboy football for Cardiff City for seven years before being released and went on to spend two years with South Gloucestershire and Stroud College, playing for the College side and Bristol Rovers' under-18 team. After finishing at South Gloucestershire and Stroud College he signed his first professional contract with Rovers during the summer of 2008, ahead of the start of the 2008–09 season. He joined Southern Football League Division One South & West side Taunton Town on loan in September 2008, making his debut in a 4–0 defeat away at Gosport Borough. Swallow made five appearances for Taunton in all competitions before signing for Bridgwater Town of the Southern Football League Division One South & West on a one-month loan in November. He started a one-month loan with Southern Football League Premier Division side Chippenham Town on 20 February 2009. Swallow started his fourth and final loan of the season after joining Southern Football League Premier Division side Mangotsfield United in April.
Swallow had earned much praise for his pre-season performances in 2009, and his senior debut came on 11 August, when he played in a League Cup first round tie against Aldershot Town, coming on as a 73rd minute substitute for Sean Rigg.
On 9 November 2010, Swallow scored his first senior goal for the club in a 6–3 win over Wycombe Wanderers in the Football League Trophy. He scored his second goal for Rovers in the next round of the Football League Trophy against Exeter City.
On 31 August 2011, Swallow joined Conference Premier side Bath City on a three-month loan. After making nine appearances for Bath he was recalled by Rovers on 16 November because of injury problems in the team.
On 4 December, Swallow came on as a second-half substitute against AFC Totton in the FA Cup second round. Rovers were 4–1 up, and Swallow was sent off for a reckless challenge after just six minutes, which drew criticism from manager Paul Buckle, although Rovers went on to win 6–1. Later that month he was told he could leave the club on a free transfer. Conference Premier side York City made a failed attempt to sign Swallow during January 2012, before he was released by Rovers after his contract was cancelled by mutual consent on 31 January.
Swallow eventually signed for York on a contract until the end of the 2011–12 season on 2 February 2012. He made his debut in York's 1–0 victory at home to Ebbsfleet United in the FA Trophy third round on 14 February. Swallow was released by York on 13 April 2012 because of an internal issue reported as his lack of punctuality at training sessions.
On 10 August 2012, Swallow signed for Conference Premier club Newport County on an initial one-month contract which was subsequently extended. He was part of the Newport team that reached the Conference Premier play-offs in the 2012–13 season, in which he made 23 appearances and scored 2 goals. Swallow was not part of the matchday squad as Newport won the 2013 Conference Premier play-off Final versus Wrexham at Wembley Stadium 2–0 to return to the Football League after a 25-year absence with promotion to League Two. He was released by Newport on 11 May 2013.
He joined Conference South team Bromley on 10 September 2013 following a successful trial. He made his debut as a second-half substitute in a 3–0 win over Staines Town on 14 September 2013. Following further substitute appearances in victories against Concord Rangers and Basingstoke Town, his first start for the club came in the FA Cup Second qualifying round against Burgess Hill Town on 28 September 2013. Bromley went on to win the match 1-0, with Swallow providing the assist for the goal, scored by Shamir Mullings. He scored his first goal for Bromley on 5 October 2013, in a 1-1 away draw with Boreham Wood. He left the club on 13 January 2014, having made 15 appearances in all competitions and scoring one goal.
On 20 January 2014, Swallow signed for Dartford, and was given the number 19 shirt. He made his debut in a 5-1 win over Woking on 18 February, coming on as an 86th-minute substitute. In May 2014, Swallow was released by Dartford after spending six months with the club, making eleven appearances.
In July 2014 trailed with Havant & Waterlooville F.C. and played 45 minutes on 10 July against Horndean FC. He was than after successful trial signed on 11 July 2014 by the Hawks.
Swallow was called up to the Wales semi-professional squad for the match versus Turkey in October 2012 and made his debut in the starting line-up.
Swallow plays primarily as a left winger and can also operate at left back. He has been praised for his crossing ability, his ability to hold the ball up and his workrate.As of match played 26 April 2014.