Navigating healthcare systems can be complex and overwhelming, creating barriers for patients seeking timely and appropriate medical attention. In this paper, we introduce C-PATH (Conversational Patient Assistance and Triage in Healthcare), a novel conversational AI system powered by large language models (LLMs) designed to assist patients in recognizing symptoms and recommending appropriate medical departments through natural, multi-turn dialogues. C-PATH is fine-tuned on medical knowledge, dialogue data, and clinical summaries using a multi-stage pipeline built on the LLaMA3 architecture. A core contribution of this work is a GPT-based data augmentation framework that transforms structured clinical knowledge from DDXPlus into lay-person-friendly conversations, allowing alignment with patient communication norms. We also implement a scalable conversation history management strategy to ensure long-range coherence. Evaluation with GPTScore demonstrates strong performance across dimensions such as clarity, informativeness, and recommendation accuracy. Quantitative benchmarks show that C-PATH achieves superior performance in GPT-rewritten conversational datasets, significantly outperforming domain-specific baselines. C-PATH represents a step forward in the development of user-centric, accessible, and accurate AI tools for digital health assistance and triage.