Internet of medical things (IoMT) has made it possible to collect applications and medical devices for improving healthcare information technology. Today, limitations in technology enable COVID-19 call centers to restrict the number of calls per day. To this end, the unprecedented virality of COVID-19 makes call centers to be likely overstressed. Thus, people who are tested for COVID-19 virus may not get adequate guidance to manage and minimize both its risk and transmission. In addition, lack of patients privacy has restricted the sharing of COVID-19 data among health institutions. To resolve the above mentioned limitations, this paper proposes privacy infrastructure based on federated learning and blockchain technology. The proposed infrastructure has the potentials to enhance public communication and deliver alternative methods to disseminate COVID-19 information. Also, the proposed infrastructure can effectively resolve the issue of large data silos and provide a shared model while preserving the privacy of data owners. Furthermore, information security and privacy analyses show that the proposed infrastructure is robust against information security related attacks.