Distantly-Supervised Named Entity Recognition (DS-NER) effectively alleviates the burden of annotation, but meanwhile suffers from the label noise. Recent works attempt to adopt the teacher-student framework to gradually refine the training labels and improve the overall robustness. However, we argue that these teacher-student methods achieve limited performance because the poor calibration of the teacher network produces incorrectly pseudo-labeled samples, leading to error propagation. Therefore, we attempt to mitigate this issue by proposing: (1) Uncertainty-Aware Teacher Learning that leverages the prediction uncertainty to reduce the number of incorrect pseudo labels in the self-training stage; (2) Student-Student Collaborative Learning that allows the transfer of reliable labels between two student networks instead of indiscriminately relying on all pseudo labels from its teacher. This approach further enables a full exploration of mislabeled samples rather than simply filtering unreliable pseudo-labeled samples. We evaluate our proposed method on five DS-NER datasets, demonstrating that our method is superior to the state-of-the-art DS-NER denoising methods.