Large Language Models (LLMs) have rapidly become important tools in Biomedical and Health Informatics (BHI), enabling new ways to analyze data, treat patients, and conduct research. This study aims to provide a comprehensive overview of LLM applications in BHI, highlighting their transformative potential and addressing the associated ethical and practical challenges. We reviewed 1,698 research articles from January 2022 to December 2023, categorizing them by research themes and diagnostic categories. Additionally, we conducted network analysis to map scholarly collaborations and research dynamics. Our findings reveal a substantial increase in the potential applications of LLMs to a variety of BHI tasks, including clinical decision support, patient interaction, and medical document analysis. Notably, LLMs are expected to be instrumental in enhancing the accuracy of diagnostic tools and patient care protocols. The network analysis highlights dense and dynamically evolving collaborations across institutions, underscoring the interdisciplinary nature of LLM research in BHI. A significant trend was the application of LLMs in managing specific disease categories such as mental health and neurological disorders, demonstrating their potential to influence personalized medicine and public health strategies. LLMs hold promising potential to further transform biomedical research and healthcare delivery. While promising, the ethical implications and challenges of model validation call for rigorous scrutiny to optimize their benefits in clinical settings. This survey serves as a resource for stakeholders in healthcare, including researchers, clinicians, and policymakers, to understand the current state and future potential of LLMs in BHI.