This study represents the first integration of large language models (LLMs) with non-negative matrix factorization (NMF), marking a novel advancement in the source separation field. The LLM is employed in two unique ways: enhancing the separation results by providing detailed insights for disease prediction and operating in a feedback loop to optimize a fundamental frequency penalty added to the NMF cost function. We tested the algorithm on two datasets: 100 synthesized mixtures of real measurements, and 210 recordings of heart and lung sounds from a clinical manikin including both individual and mixed sounds, captured using a digital stethoscope. The approach consistently outperformed existing methods, demonstrating its potential to significantly enhance medical sound analysis for disease diagnostics.