Medical image captioning via vision-language models has shown promising potential for clinical diagnosis assistance. However, generating contextually relevant descriptions with accurate modality recognition remains challenging. We present DualPrompt-MedCap, a novel dual-prompt enhancement framework that augments Large Vision-Language Models (LVLMs) through two specialized components: (1) a modality-aware prompt derived from a semi-supervised classification model pretrained on medical question-answer pairs, and (2) a question-guided prompt leveraging biomedical language model embeddings. To address the lack of captioning ground truth, we also propose an evaluation framework that jointly considers spatial-semantic relevance and medical narrative quality. Experiments on multiple medical datasets demonstrate that DualPrompt-MedCap outperforms the baseline BLIP-3 by achieving a 22% improvement in modality recognition accuracy while generating more comprehensive and question-aligned descriptions. Our method enables the generation of clinically accurate reports that can serve as medical experts' prior knowledge and automatic annotations for downstream vision-language tasks.