Nowadays, blockchain-based healthcare systems have gained more attention for handling a huge amount of patient health data observed by Internet-of-Things (IoT) systems. Several studies have focused on integrating blockchain technology with healthcare systems to ensure the secrecy and transparency of patient data. Among these, an enhanced eHealthChain system has been designed, which comprises Enhanced OAuth (EOAuth) 2.0 to enhance user security based on their trust score. It also applies a Constrained Application Protocol (CoAP) to achieve reliable transmission by controlling congestion in the network according to the Retransmission Timeout (RTO). However, the CoAP causes long inactive latency in the network, and the backoff values are constant, which do not differ in dynamic network settings. Hence, this article proposes an Enhanced CoAP (ECoAP), which adopts adaptive RTO estimation with an Adaptive Backoff Factor (ABF), Data Loss Rate (DLR) estimation, and a Refined Random Early Identification (RREI) scheme for Congestion Control (CC) in dynamic network configurations. This can be useful to reduce the number of retransmissions by predicting the variable backoff values. Moreover, this protocol achieves effective queue management and regulation of backoff values based on congestion levels. Finally, the implementation findings exhibit that the ECoAP outperforms the classical CoAP for secure and reliable transmission in blockchain-enabled clinical IoT systems. The results revealed that the proposed system achieves 24.6% unsuccessful transmissions, 4.64 seconds average service time, 0.2264 seconds average network delay, 94.96% average server usage, 16.9% average Quality of Experience (QoE), 92.4% confidentiality, 86.5% authorization, and 93.9% data integrity for 2500 transmissions.