This paper introduces a novel methodology for constructing a comprehensive biomedical knowledge graph by applying advanced Natural Language Processing (NLP) techniques. By leveraging Large Language Models (LLMs) and a multifaceted prompt engineering approach, we effectively perform Named Entity Recognition (NER) and Relation Extraction (RE) on biomedical literature, targeting entities such as diseases, drugs, proteins, procedures, and symptoms. Our methodology incorporates eight distinct prompt engineering strategies for NER and a standardized approach for RE, facilitating the extraction of intricate inter-entity relationships. The resulting knowledge graph amalgamates diverse data sources into a unified framework, enabling efficient querying, visualization, and analysis of biomedical information. Furthermore, we present an innovative query processing pipeline that integrates GPT-3.5 turbo with the knowledge graph, allowing users to interact with the graph through natural language. This integrated system empowers the discovery of novel correlations, accelerating scientific research and fostering interdisciplinary collaboration. This represents a substantial contribution to the field of biomedical knowledge graph construction, offering a robust platform for accelerating scientific discovery and informing clinical decision-making.