Intelligent medical image analysis is essential for clinical decision support but is often limited by scarce annotations, constrained computational resources, and suboptimal model generalization. To address these challenges, we propose a lightweight medical image classification framework that integrates self-supervised contrastive learning with quantum-enhanced feature modeling. MobileNetV2 is employed as a compact backbone and pretrained using a SimCLR-style self-supervised paradigm on unlabeled images. A lightweight parameterized quantum circuit (PQC) is embedded as a quantum feature enhancement module, forming a hybrid classical-quantum architecture, which is subsequently fine-tuned on limited labeled data. Experimental results demonstrate that, with only approximately 2-3 million parameters and low computational cost, the proposed method consistently outperforms classical baselines without self-supervised learning or quantum enhancement in terms of Accuracy, AUC, and F1-score. Feature visualization further indicates improved discriminability and representation stability. Overall, this work provides a practical and forward-looking solution for high-performance medical artificial intelligence under resource-constrained settings.