The rapid expansion of mobile apps on Android platforms, particularly AI-based medical chatbots, presents both remarkable opportunities and significant privacy challenges within the healthcare sector. This paper explores the complex privacy issues arising from the use of such chatbots, focusing on the sensitive nature of health information exchange. We critically assess the effectiveness of current dynamic analysis techniques and the limitations they face in addressing the unique privacy concerns associated with medical chatbots, including third-party integration, encryption of user interactions, and data sharing practices. Our research introduces a novel methodology that employs network packet capture and analysis, using the HTTP Toolkit to scrutinize data traffic between mobile apps and servers in real-time. Through the detailed examination of HAR files and the incorporation of ChatGPT 4.0, our study provides insights into the web interactions and data handling processes of AI-based medical chatbots.