Local class imbalance and data heterogeneity across clients often trap prototype-based federated contrastive learning in a prototype bias loop: biased local prototypes induced by imbalanced data are aggregated into biased global prototypes, which are repeatedly reused as contrastive anchors, accumulating errors across communication rounds. To break this loop, we propose Confidence-Aware Federated Contrastive Learning (CAFedCL), a novel framework that improves the prototype aggregation mechanism and strengthens the contrastive alignment guided by prototypes. CAFedCL employs a confidence-aware aggregation mechanism that leverages predictive uncertainty to downweight high-variance local prototypes. In addition, generative augmentation for minority classes and geometric consistency regularization are integrated to stabilize the structure between classes. From a theoretical perspective, we provide an expectation-based analysis showing that our aggregation reduces estimation variance, thereby bounding global prototype drift and ensuring convergence. Extensive experiments under varying levels of class imbalance and data heterogeneity demonstrate that CAFedCL consistently outperforms representative federated baselines in both accuracy and client fairness.