We propose to use Inter Vehicle Communications as part of a distributed system for ubiquitous health monitoring of patients. The biomedical data will be collected by wearable health diagnostic devices, which include various types of sensors. When patients are traveling on highways, we propose to transmit the measured biomedical data towards the corresponding Health Monitoring Centers via a Inter Vehicle Communication Network, which will guarantee the needed reliability, especially in areas where other wireless communications are not available. In particular, it is important that the Inter Vehicle Communication Network provides different priorities to various types of messages, depending on their urgency. We extend, a previously proposed inter vehicle hierarchical routing protocol, with priority scheduling to provide the needed priority services. We study various scheduling techniques and compare their effects on the service.