Federated learning (FL) is a distributed framework for collaboratively training with privacy guarantees. In real-world scenarios, clients may have Non-IID data (local class imbalance) with poor annotation quality (label noise). The co-existence of label noise and class imbalance in FL's small local datasets renders conventional FL methods and noisy-label learning methods both ineffective. To address the challenges, we propose FedCNI without using an additional clean proxy dataset. It includes a noise-resilient local solver and a robust global aggregator. For the local solver, we design a more robust prototypical noise detector to distinguish noisy samples. Further to reduce the negative impact brought by the noisy samples, we devise a curriculum pseudo labeling method and a denoise Mixup training strategy. For the global aggregator, we propose a switching re-weighted aggregation method tailored to different learning periods. Extensive experiments demonstrate our method can substantially outperform state-of-the-art solutions in mix-heterogeneous FL environments.