Machine learning-assisted diagnosis shows promise, yet medical imaging datasets are often scarce, imbalanced, and constrained by privacy, making data augmentation essential. Classical generative models typically demand extensive computational and sample resources. Quantum computing offers a promising alternative, but existing quantum-based image generation methods remain limited in scale and often face barren plateaus. We present MediQ-GAN, a quantum-inspired GAN with prototype-guided skip connections and a dual-stream generator that fuses classical and quantum-inspired branches. Its variational quantum circuits inherently preserve full-rank mappings, avoid rank collapse, and are theory-guided to balance expressivity with trainability. Beyond generation quality, we provide the first latent-geometry and rank-based analysis of quantum-inspired GANs, offering theoretical insight into their performance. Across three medical imaging datasets, MediQ-GAN outperforms state-of-the-art GANs and diffusion models. While validated on IBM hardware for robustness, our contribution is hardware-agnostic, offering a scalable and data-efficient framework for medical image generation and augmentation.