The Internet of Medical Things (IoMT), combined with interconnected wearable devices and medical-grade sensors, can play an essential role in healthcare evolution. By exploiting the data generated by the plethora of interconnected devices (vital parameters, location-based info, patients activity and more), advanced ICT systems can be put in place with predicting capabilities. This way potentially critical situations, that may evolve in serious complications to patients’ well-being, can be promptly recognized and successfully addressed, first of all, to save lives and secondarily to limit economical damages. To support continuous patient monitoring in public and private healthcare, this paper proposes "DILoCC", an architecture to manage wearable devices, sensors and applications, that uses a Distributed Incremental Learning (DIL) approach to exploit cooperation among the sensing devices and increase the overall system efficiency through the mitigation of "Catastrophic Forgetting" consequences.