Large language models (LLMs) exhibit extensive medical knowledge but are prone to hallucinations and inaccurate citations, which pose a challenge to their clinical adoption and regulatory compliance. Current methods, such as Retrieval Augmented Generation, partially address these issues by grounding answers in source documents, but hallucinations and low fact-level explainability persist. In this work, we introduce a novel atomic fact-checking framework designed to enhance the reliability and explainability of LLMs used in medical long-form question answering. This method decomposes LLM-generated responses into discrete, verifiable units called atomic facts, each of which is independently verified against an authoritative knowledge base of medical guidelines. This approach enables targeted correction of errors and direct tracing to source literature, thereby improving the factual accuracy and explainability of medical Q&A. Extensive evaluation using multi-reader assessments by medical experts and an automated open Q&A benchmark demonstrated significant improvements in factual accuracy and explainability. Our framework achieved up to a 40% overall answer improvement and a 50% hallucination detection rate. The ability to trace each atomic fact back to the most relevant chunks from the database provides a granular, transparent explanation of the generated responses, addressing a major gap in current medical AI applications. This work represents a crucial step towards more trustworthy and reliable clinical applications of LLMs, addressing key prerequisites for clinical application and fostering greater confidence in AI-assisted healthcare.