For telemedicine, Wireless Body Area Network (WBAN) offers enormous benefits where a patient can be remotely monitored without compromising the mobility of remote treatments. With the advent of high capacity and reliable wireless networks, WBANs are used in several remote monitoring systems, limiting the COVID-19 spread. The sensitivity of telemedicine applications mandates confidentiality and privacy requirements. In this paper, we propose a secure WBAN-19 telemedicine system to overcome the pervasiveness of contagious deceases utilizing a novel aggregate identity-based signcryption scheme with an equality test feature. We demonstrate a security analysis regarding indistinguishable adaptive chosen-ciphertext attack (IND-CCA2), one-way security against adaptive chosen-ciphertext attack (OW-CCA2), and unforgeability against adaptive chosen-message attack (EUF-CMA) under the random oracle model. The security analysis of the scheme is followed by complexity evaluations where the computation cost and communication overhead are measured. The evaluation demonstrates that the proposed model is efficient and applicable in telemedicine systems with high-performance capacities.