Current prompt-based and adapter-based tuning of vision-language models (VLMs) is attractive for medical imaging, where clinical data sensitivity favors frozen backbones and annotations are limited. However, these methods typically optimize only the ground-truth class, treating all other classes as equally incorrect, ignoring clinically meaningful class relations and yielding unstable decision boundaries in limited-supervision settings. We propose Omni-Geometry Knowledge Distillation (OGKD), a new framework that injects class-relation structure into the teacher to produce directional targets that preserve the ground truth while respecting inter-class geometry. Using these targets, we develop two distillation losses: Global Geometry-Aware Distillation (GAD) operates on the global image token, and Label-Guided Geometry Distillation (LGD) applies the same geometry to attentive patch tokens to improve fine-grained alignment. Across comprehensive experiments and analyses on 11 widely-used medical datasets for base-to-novel and few-shot evaluations, our OGKD achieves substantially better performance, consistently improving accuracy by an average absolute gain of 1.7%-2.8% over all prior state-of-the-art VLM adaptation counterparts. It also robustly generalizes to unseen classes and yields more reliable predictions than other approaches. Our code is available at https://github.com/tientrandinh/OGKD.