Through IoT, humans and objects can be connected seamlessly, to guaranty improved quality of service (QoS). IoT-driven e-Health systems benefit from such rich network setting, to transmit health information and deliver health services. It is expected to grow massively in scale, but for that to happen, several issues need to be addressed, including security and trust. Edge computing paradigms, such as Fog computing and Cloudlet, are already popular in IoT based e-Health domain. Fog nodes are leveraged to reduce latency between IoT devices and remote cloud computing infrastructure. In this work, we explain how Mobile edge-clouds, which is a less popular edge computing paradigm, can be employed to achieve similar or lower latency, at a lower cost. We also propose a lightweight mechanism for security and fairness in e-Health protocols that are based on mobile edge-clouds and other paradigms. Detailed simulation experiments show that the proposed method is scalable and can efficiently mitigate attacks that are targeted at e-Health information and the network.