Internet of Things (IoT) generates a myriad amount of data, which is sent over the Cloud computing infrastructure for analytics and Business Intelligence. This application scenario suffers network delays, transmission delays and delays in decision making. Due to these drawbacks, the Cloud-based IoT infrastructure is not suitable for time-critical health care applications. To overcome this problem, a smart way is introduced called “Fog Computing” - a LAN based processing approach which has multiple advantages. When IoT, Fog and Cloud Computing are combined, the resultant system’s performance is far better. Hence, the combination results in a very efficient Health Care system. Fog and Cloud Computing have their dimensions that not only support each other but also explore many new application domains. In this paper, the real-time ElectroCardioGram (ECG) based Health Care system is implemented in Cloud and Fog Computing. Different Quality of Service (QoS) parameters like memory consumption, transmission delays, computation delays, network delays, Carbon dioxide emission, data transferred and response time are measured, analyzed and improved to make the system more efficient. Based on the Fog computing characteristics and capabilities, the Raspberry Pi 3 B+ model is configured as a Health Care serving gateway by using different installation and configuration steps. Initially, the proposed system is tested for one patients ECG data analysis over cloud and Fog. In every set up all QoS parameters are measured and later the system is subjected to multiple ECG streams for varying numbers of patients to find the limitations of the Raspberry Pi node as a Fog Computing node. The obtained results show that for more number of ECG streams the Fog node is not able maintain QoS in decision making time. Every QoS parameter is explored in detail for decision-making time. In the end, the Fog computing based proposed system is concluded for its pros and cons and future aspects of the Fog node are discussed to make better systems.