We study the problem of training named entity recognition (NER) models using only distantly-labeled data, which can be automatically obtained by matching entity mentions in the raw text with entity types in a knowledge base. The biggest challenge of distantly-supervised NER is that the distant supervision may induce incomplete and noisy labels, rendering the straightforward application of supervised learning ineffective. In this paper, we propose (1) a noise-robust learning scheme comprised of a new loss function and a noisy label removal step, for training NER models on distantly-labeled data, and (2) a self-training method that uses contextualized augmentations created by pre-trained language models to improve the generalization ability of the NER model. On three benchmark datasets, our method achieves superior performance, outperforming existing distantly-supervised NER models by significant margins.