The integration of Large Language Models (LLMs) into healthcare diagnostics offers a promising avenue for clinical decision-making. This study outlines the development of a novel method for zero-shot/few-shot in-context learning (ICL) by integrating medical domain knowledge using a multi-layered structured prompt. We also explore the efficacy of two communication styles between the user and LLMs: the Numerical Conversational (NC) style, which processes data incrementally, and the Natural Language Single-Turn (NL-ST) style, which employs long narrative prompts. Our study systematically evaluates the diagnostic accuracy and risk factors, including gender bias and false negative rates, using a dataset of 920 patient records in various few-shot scenarios. Results indicate that traditional clinical machine learning (ML) models generally outperform LLMs in zero-shot and few-shot settings. However, the performance gap narrows significantly when employing few-shot examples alongside effective explainable AI (XAI) methods as sources of domain knowledge. Moreover, with sufficient time and an increased number of examples, the conversational style (NC) nearly matches the performance of ML models. Most notably, LLMs demonstrate comparable or superior cost-sensitive accuracy relative to ML models. This research confirms that, with appropriate domain knowledge and tailored communication strategies, LLMs can significantly enhance diagnostic processes. The findings highlight the importance of optimizing the number of training examples and communication styles to improve accuracy and reduce biases in LLM applications.