The holistic concept of smart cities has been adopted to increase economic, environmental, and social sustainability. For the sustainable health of a smart city inhabitant, there is a requirement for innovations in implementing health solutions. Given the exponential growth of the Internet of Health Things (IoHT) in health infrastructures, bulk amounts of health-related data are accumulated in Personal Health Records (PHR) and processed in storage data centers. One of the major challenges in this scenario is the security of this enormous medical data. The conventional encryption schemes generate single cipher images making the cryptosystem vulnerable to single-point attacks. This paper evaluates a distributed security module for the clinical images that form 80% of the health data. We utilize the Rivest Cipher 6 (RC6) encryption algorithm with a Computational Secret Sharing Scheme (CSIS) for distributed storage of clinical images. The key is shared using a Perfect Secret Sharing (PSS) scheme. We show that (k-1) key-shares and the 'n' image shares can be made public because of the perfect security of the scheme. The rest of the key shares can be secured using the Deoxyribonucleic Acid substitution (DNA substitution) method. Analysis of the shares generated reveals the strength of the cryptosystem and gives an insight into the degree of security provided to the health-related data. The entropy of the generated shares is higher than 7.99, and structural similarity (SSIM) values are negligible. The Number of Pixels Change Rate (NPCR) values are greater than 99.55% for all the shares that show a high diffusion measure. Comparison with state-of-the-art schemes reveals and validates the robustness of the cryptosystem.