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Sheedy made his Championship debut for Dublin against Meath in the first round of the Leinster Senior Football Championship in 1991,after having been a panellest on the Dublin team beaten by Kerry in 1984.0 The series famously finished after four games (three replays), with Dublin losing by a point. He scored a goal in the opening game against Meath and finished the series with 1-03. He went on to win five Leinster championships with Dublin in 1984,1992, 1993, 1994 and 1995. He won an allstar for Dublin in 1994, the same year that he won his fourth Lenster championship and then an all-Ireland senior football final defeat to Down; a game which finished on a scoreline of 0–13 to 1–12.He suffered a cruciate ligament injury in 1995,ruling him out of an allIreland medal with Dublin that year.
Sheedy won two national football league finals with Dublin. The first final was against Kildare in his first senior football year. He then won his second title in 1993 against Donegal in a game that was forced to a replay which Dublin eventually won. Sheedy also won a North American championship with the Wolfe Tones Gaa club in Chicago in 1997 a team that included Kevin o Brien of Wicklow and Gregory Macarton of Down. Sheedy won the All-Ireland Masters Football Championship with Dublin in 2004 when he captained Dublin to victory over Leitrim.
Sheedy was manager of the Edenderry senior team in County Offaly. He won a Division Two League title as manager of Edenderry in June 2009. On 7 December, he resigned from managing Edenderry. He is now managing Moorefield of Kildare and won the Kildare Senior Championship on 17 October 2010.
In October 2013, Sheedy was confirmed as the new manager of the Longford Senior Football team.