Wireless body area network (WBAN) is an emerging technology for remotely monitoring the critically affected patients regularly, which is a utility platform for a medical pandemic like COVID-19. IEEE 802.15.6 medium access control (MAC) defines the communication standard to pillar the quality requirements of the sensor nodes. Most of the existing works are focused on optimizing the conventional MAC by adopting dynamic scheduled access and efficient contention scheme to utilize the superframe structure. However, utilizing the entire slots based on demand from different priority sensor nodes is a challenging task. To address this issue, an efficient time slot allocation method, namely the demand-based dynamic slot allocation (DDSA) algorithm, is proposed. DDSA computes sensor node priority based on the run-time parameters such as critical index, remaining energy, and delivery demand. The slot assignment is proportional to the priority order, and the critical index factor resolves slot conflict. This guarantees data priority preservation with fair allocation for critical and non-critical medical data. The simulation is carried out using the Castalia-OMNeT++ simulator, and the results are shown that the proposed DDSA algorithm outperforms priority-based MAC and the conventional method in terms of packet reception rate, energy efficiency, and latency.