The challenge of addressing mixed closed-set and open-set label noise in medical image classification remains largely unexplored. Unlike natural image classification where there is a common practice of segregation and separate processing of closed-set and open-set noisy samples from clean ones, medical image classification faces difficulties due to high inter-class similarity which complicates the identification of open-set noisy samples. Moreover, prevailing methods do not leverage the full potential of open-set noisy samples for label noise mitigation, often leading to their exclusion or application of uniform soft labels. To address these issues, we propose an Extended Noise-robust Contrastive and Open-set Feature Augmentation (ENCOFA) framework. ENCOFA includes the Extended Noise-robust Supervised Contrastive (ENSC) Loss, which aids in distinguishing features across classes. The ENSC loss regards open-set noisy samples as an extended class and mitigates label noise by weighting contrastive pairs with label reliability. Furthermore, we develop an Open-set Feature Augmentation (OSFeatAug) module that enriches the features of open-set samples, utilizing the model's extra capacity to prevent overfitting to noisy data. We conducted experiments on a synthetic noisy dataset and a real-world noisy dataset. Our results indicate the superiority of ENCOFA and the effectiveness of leveraging the open-set noisy samples to combat label noise.