Accurate medical diagnosis often relies on both textual self-reported symptoms and structured medical examination results of patients. However, these examinations vary significantly in cost—measured in time, money, or patient discomfort---creating a challenging trade-off between diagnostic accuracy and resource efficiency. To address this issue, we propose a dynamic diagnostic framework that incrementally selects medical examinations based on individual characteristics of each patient. Starting with textual self-reported symptoms and basic demographic, the system determines follow-up examinations step-by-step, improving accuracy while minimizing additional costs. Specifically, we introduce DISC—— $\textbf{D}$ynamic feature selection with $\textbf{I}$nstance-$\textbf{S}$pecific $\textbf{C}$ost sensitivity——a multimodal framework that integrates unstructured textual self-reported symptoms and structured medical examination data. DISC treats each examination as a feature and learns to acquire them sequentially to optimize predictive performance under personalized cost constraints. Experiments on three real-world hospital datasets demonstrate that DISC outperforms existing feature selection baselines, achieving substantial cost reductions while maintaining high diagnostic accuracy. These results highlight the potential of DISC for practical deployment in cost-sensitive clinical decision-making. We evaluate DISC on three real-world datasets collected from hospitals, where it achieves state-of-the-art performance compared to existing methods.