Ensuring good health and well-being is one of the crucial Sustainable Development Goals (SDGs) that aims to promote healthy lives and well-being for people of all ages. This involves providing affordable and environmentally friendly medical services to the public fairly and equitably. Good health and well-being goals include achieving fair health outcomes and strong healthcare systems. It also highlights the importance of integrating sustainable health considerations into the policy frameworks of developing countries, which are established to address the social factors that influence health. Regarding healthcare reform, Information and Communication Technologies (ICTs) play a pivotal role as key enablers to improve patient access, treatment quality, and system efficiency. This shift in focus also highlights the significance of fostering digital accessibility, sustainability, inventiveness, cybersecurity, and digital leadership. Nevertheless, incorporating progressively advancing ICT technology into healthcare systems, sometimes called digital transformation, is not simple. However, some challenges arise in integration, application design, and security measures. While numerous studies have been suggested to tackle incorporating ICT technologies into healthcare systems, these studies have had limited scope and have not considered several factors. Therefore, there is a pressing need for an extensive research study focusing on integration technologies, design challenges, security and privacy challenges, application areas, and the potential positive and negative effects. Therefore, this paper contributes as the research literature study covering an important SDG, “Good health and well-being,” and its digital transformation, along with summarising our research findings in a detailed and taxonomical way. First, we analyze an all-encompassing taxonomy of prior research on healthcare and well-being, emphasizing incorporating ICT in healthcare, specifically with sustainability, security and privacy challenges, design and integration challenges, applications associated with Electronic Health (E-Health), and potential future avenues for exploration. Then, we explore the need for digital transformation in healthcare and its significant components, highlight E-Health’s importance and benefits, explore its integration and design challenges, and categorize the security and privacy challenges. Next, we determine the role of Blockchain Technology as today’s leading technology in E-Health. We discuss Blockchain Technology and its characteristics, highlight its benefits, and describe the possible types of Blockchain-based E-Health use cases. Furthermore, we compare the positive and negative impacts of ICT integration and identify open issues and challenges of integrating ICT technologies into the healthcare systems. We also discuss future research directions, strengthening researchers to address the issues in future solutions.