This paper explores a content-based image retrieval (CBIR) system for radiologists who struggle to efficiently retrieve similar cases due to the increasing volume of medical images. Building on existing CBIR research for tumor characterization, this study advances CBIR research for 3D medical images through three key contributions. First, we present a framework compatible with large-scale, unstructured image storage systems such as PACS in real-world clinical settings by eliminating the reliance on pre-segmented data and organ-specific datasets. Second, we propose C-MIR, a novel 3D reranking method that applies the context-sensitive late interaction mechanism of ColBERT to 3D medical images. Third, we perform a comprehensive evaluation on four tumor regions using three feature extractors and three database configurations. The results highlight the significant advantages of C-MIR, demonstrating significant performance improvements (p<0.05) for colon and lung cancers. C-MIR also shows potential for improving tumor staging, suggesting the need for future research. Ultimately, this research aims to bridge the gap between advanced search technologies and practical applications in healthcare, paving the way for improved diagnostic processes.