The prompt evolution of Internet of Medical Things (IoMT) promotes pervasive in-home health monitoring networks. However, excessive requirements of patients result in insufficient spectrum resources and communication overload. Mobile Edge Computing (MEC) enabled 5G health monitoring is conceived as a favorable paradigm to tackle such an obstacle. In this paper, we construct a cost-efficient in-home health monitoring system for IoMT by dividing it into two sub-networks, i.e., intra-Wireless Body Area Networks (WBANs) and beyond-WBANs. Highlighting the characteristics of IoMT, the cost of patients depends on medical criticality, Age of Information (AoI) and energy consumption. For intra-WBANs, a cooperative game is formulated to allocate the wireless channel resources. While for beyond-WBANs, considering the individual rationality and potential selfishness, a decentralized non-cooperative game is proposed to minimize the system-wide cost in IoMT. We prove that the proposed algorithm can reach a Nash equilibrium. In addition, the upper bound of the algorithm time complexity and the number of patients benefiting from MEC is theoretically derived. Performance evaluations demonstrate the effectiveness of our proposed algorithm with respect to the system-wide cost and the number of patients benefiting from MEC.