Natural disasters like earthquakes and tsunami could destroy the existing infrastructure-based communication system. IoT-based health monitoring is not possible in such scenarios. Therefore, there is a need for other resilient health monitoring frameworks to provide consistent health monitoring without depending on existing communication platforms. Wireless Body Sensor Network (WBSN) based health monitoring utilizing Vehicular Ad-hoc Network (VANET) as a communication medium could be a handy solution for transmitting patients' health information to the nearest ambulance or hospital in emergencies or disaster-prone areas. Casualty rates can be reduced significantly by providing emergency treatment to injured patients within a stipulated time. VANET's health monitoring applications are time-critical; therefore, designing a stable and efficient routing algorithm is a significant research challenge. Over the years, the researchers proposed many routing solutions to minimize the delay for critical applications. This paper proposed a Weighted Geographical Routing (W-GeoR) for VANET's health monitoring applications focusing on next-hop node selection for faster vital signs dissemination to facilitate post-disaster health monitoring in urban traffic environments. The proposed protocol utilized traffic-aware information including traffic mobility, inter-vehicle distances, speed differences, communication link expiration time, channel quality, and proximity factors for optimal next-hop node selection procedure. W-GeoR is tested on a postdisaster scenario created with SUMO-0.32 and NS-3.23 platforms. Simulated results confirm that W-GeoR performs better than the existing state-of-the-art protocols.