Health care services have become a high demand due to the rise in medical technology. As a result, related resources are being depleted. Hospitals no longer have any space to accommodate for incoming patients. Remote Patient Monitoring (RPM) is a solution to this issue by creating a convenient and easy to access healthcare service. However, RPM systems are constrained by issues on data integrity, patient privacy and response time. The integrity of data is key for RPM systems to accurately detect emergencies. Patients emphasize their privacy, which requires health care services to maintain the confidentiality of their patient's information. Wearable health monitors continuously transmit data. This results in high volumes of data that enters the servers. In this paper, we propose an architecture that uses Fog-IoT to an already existing RPM system and addresses these three issues. The introduced system enables the health care providers to verify any of their data through a local server before it is reported to the server. Also, this design incorporates a data filter that controls the outgoing data to maintain patient privacy. Finally, the inclusion of a local server offloads the extra data processing that is required from the server for a better flow of data. Tests in latency were executed to investigate the feasibility of a scalable fog architecture against a standard cloud-device setup. The results show that the proposed fog setup yielded significantly lower latencies under an increasing number of RPM rooms compared to the cloud setup. This result further supports, the fog-IoT as a potential option for a scalable RPM architecture. Overall, this framework makes improvements towards making RPM systems a more ideal means for health care services in managing data.