In healthcare applications, numerous sensors and devices produce massive amounts of data which are the focus of critical tasks. Their management at the edge of the network can be done by Fog computing implementation. However, Fog Nodes suffer from lake of resources That could limit the time needed for final outcome/analytics. Fog Nodes could perform just a small number of tasks. A difficult decision concerns which tasks will perform locally by Fog Nodes. Each node should select such tasks carefully based on the current contextual information, for example, tasks' priority, resource load, and resource availability. We suggest in this paper a Multi-Agent Fog Computing model for healthcare critical tasks management. The main role of the multi-agent system is mapping between three decision tables to optimize scheduling the critical tasks by assigning tasks with their priority, load in the network, and network resource availability. The first step is to decide whether a critical task can be processed locally; otherwise, the second step involves the sophisticated selection of the most suitable neighbor Fog Node to allocate it. If no Fog Node is capable of processing the task throughout the network, it is then sent to the Cloud facing the highest latency. We test the proposed scheme thoroughly, demonstrating its applicability and optimality at the edge of the network using iFogSim simulator and UTeM clinic data.