Uwom began his career in the private sector working for family-owned businesses. Between 1980 and 1985, he held the positions of filing clerk, managing director and eventually chairman of the K & K Group and the Twilight Club. In 2003, he withdrew from family business and became actively involved in politics. That same year, he participated in the PDP primaries to represent Abua–Odual federal constituency in the House of Representatives. Following his attempt at the primaries, he was invited to serve as a Special Assistant to the Governor of Rivers State Peter Odili.
In 2006, Uwom began service as Commissioner of Housing and Urban Development. He spearheaded the preparation of a draft building code for Rivers State, a draft amendment of the Physical Planning and Development Law No. 6 of 2003, a draft amendment to the Rivers State Housing and Property Development Law No.14 of 1985, and a Housing Policy for the state.
In 2007, he was put in charge of a special state government fund of ₦100,000,000 provided for the people of Abua–Odual local government area by the Odili administration. The assignment entailed superintending over a committee of 20 distinguished indigenes of the local government area for the rehabilitation and resettlement of victims and communities ravaged by violent conflict and crisis. During that assignment, he managed to enumerate and screen over 500 scholarship applicants of which 50 applicants were finally chosen for overseas scholarship. In addition, he ensured that each of the 44 communities of Abua–Odual local government area were given the sum of ₦1,000,000 each to carry out community based projects of their choice. Various sums of cash relief were also presented to victims of the crisis.
Uwom was appointed chairman of the security sub-committee of the Rivers State Transition Committee in the outgoing administration of Peter Odili that paved the way for a seamless transition to the Sir Celestine Omehia administration. In March 2009, Governor Chibuike Amaechi reappointed him as Commissioner of Housing and until his resignation in 2014, he was board member of Greater Port Harcourt City Development Authority and Rainbow Town Development Limited.