Since the outbreak of the novel coronavirus (COVID-19) disease pandemic in 2019, social distancing and quarantining have become normal practices all over the world. Frequent hospital contact visits are discouraged due to the full adoption of the above control practices. Contact-based hospital visits are now considered non-obligatory due to rapid technological advances in the areas of Internet of Things (IoT) technology, healthcare systems, and smart home automation. To this end, a real-time healthcare infrastructure called (CoronaCare) is proposed in this paper for monitoring patients' health status and receiving doctors' prescriptions while staying at home. The doctors can diagnose illnesses using the physiological health parameters collected remotely from patients through a live video conferencing-based interactive system that enables healthcare professionals to discuss with patients and help them. It would collect real-time symptom data from smartphone videos. The system is based on Multi-access Edge Computing (MEC) as an IoT infrastructure and Cloud Radio Access Network (C-RAN) in 5G cellular networks structure which enables high bandwidth and ultra-low latency for efficient patients-doctors dual real-time communication. The system is simulated and the results demonstrate high throughput and low latency as the evaluation of service time is approximately 2 seconds and the average utilization of Virtual Machines (VMs) is approximately 98% for different edge computing architectures which effectively improve the system performance.