Wireless Healthcare Sensor Network (WHSN) is a benchmarking technology deployed to levitate the quality of lives for the patients and doctors. WHSN systems must fit IEEE 802.15.6 standard for specific application criteria, unlike some standard criteria that are difficult to meet. Therefore, many security models were suggested to enhance the security of the WHSN and promote system performance. Yu and Park proposed a three-factor authentication scheme based on the smart card, biometric, and password, and their scheme can be easily employed in three-tier WHSN architecture. Furthermore, they claimed that their scheme can withstand guessing attack and provide anonymity, although, after cryptanalysis, we found that their scheme lacks both. Accordingly, we suggested a three-factor authentication scheme with better system confusion due to multiplex parametric features, hash function, and higher key size to increase the security and achieve anonymity for the connected nodes. Moreover, the scheme included initialization, authentication, re-authentication, secure node addition, user revocation, and secure data transmission via blockchain technology. The formal analysis of the scheme was conducted by BAN logic (Burrows Abadi Nadeem) and the simulation was carried out by Tamarin prover to validate that the proposed scheme is resistant to replay, session hijacking, and guessing attacks, plus it provides anonymity, perfect forward secrecy, and authentication along with the key agreement.