In this paper, we investigate a key problem of Narrowband-Internet of Things (NB-IoT) in the context of 5G with Mobile Edge Computing (MEC). We address the challenge that IoT devices may have different priorities when demanding bandwidth for data transmission in specific applications and services. Due to the scarcity of bandwidth in a MEC enabled IoT network, our objective is to optimize bandwidth allocation for a group of NB-IoT devices in a way that the group can work collaboratively to maximize their overall utility. To this end, we design an optimal distributed algorithm and use simulations to demonstrate its efficacy to effectively manage various IoT data streams in a fully distributed framework.