This paper investigates the performance of cooperative non-orthogonal multiple access (C-NOMA) in a cellular downlink system. The system model consists of a base station (BS) serving multiple users, where users with good channel quality can assist the transmissions between the BS and users with poor channel quality through either half-duplex (HD) or full-duplex (FD) device-to-device (D2D) communications. We formulate and solve a novel optimization problem that jointly determines the optimal D2D user pairing and the optimal power control scheme, where the objective is maximizing the achievable sum rate of the whole system while guaranteeing a certain quality of service (QoS) for all users. The formulated problem is a mixed-integer non-linear program (MINLP) which is generally NPhard. To overcome this issue, we reconstruct the original problem into a bi-level optimization problem that can be decomposed into two sub-problems to be solved independently. The outer problem is a linear assignment problem which can be efficiently handled by the well-known Hungarian method. The inner problem is still a non-convex optimization problem for which finding the optimal solution is challenging. However, we derive the optimal power control policies for both the HD and the FD schemes in closedform expressions, which makes the computational complexity of the inner problems polynomial for every possible pairing configurations. These findings solve ultimately the original MILNP in a timely manner that makes it suitable for real-time and low latency applications. Our simulation results show that the proposed framework outperforms a variety of proposed schemes in the literature and that it can obtain the optimal pairing and power control policies for a network with 100 users in a negligible computational time.