Artificial intelligence (AI) has shown great promise in analyzing nasal endoscopic images for disease detection. However, current AI systems require extensive expert-labeled data for each specific medical condition, limiting their applications. In this work, the challenge is addressed through two key innovations, the creation of the first large-scale pre-training dataset of nasal endoscopic images, and the development of a novel self-learning AI system specifically designed for nasal endoscopy, named NaMA-Mamba. In the proposed NaMA-Mamba model, two key technologies are utilized, which are the nasal endoscopic state space model (NE-SSM) for analyzing sequences of images and an enhanced learning mechanism (CoMAE) for capturing fine details in nasal tissues. These innovations enable the system to learn effectively from unlabeled images while maintaining high accuracy across different diagnostic tasks. In extensive testing, NaMA-Mamba achieved remarkable results using minimal labeled data, matching the performance of traditional systems that require full expert labeling while needing only 1% of the labeled data for tasks such as detecting nasal polyps and identifying nasopharyngeal cancer. These results demonstrate the potential of NaMA-Mamba to significantly improve the efficiency and accessibility of AI-assisted nasal disease diagnosis in clinical practice.