Class incremental medical image segmentation (CIMIS) aims to preserve knowledge of previously learned classes while learning new ones without relying on old-class annotations. However, existing methods 1) either adopt one-size-fits-all strategies that treat all spatial regions and feature channels equally, which may hinder the preservation of accurate old knowledge, 2) or focus solely on aligning local prototypes with global ones for old classes while overlooking their local representations in new data, leading to knowledge degradation. To mitigate the above issues, we propose Prototype-Guided Calibration Distillation (PGCD) and Dual-Aligned Prototype Distillation (DAPD) for CIMIS in this paper. Specifically, PGCD exploits prototype-to-feature similarity to calibrate class-specific distillation intensity in different spatial regions, effectively reinforcing reliable old knowledge and suppressing misleading cues from old classes. Complementarily, DAPD aligns the local prototypes of old classes extracted from the current model with both global historical prototypes and local prototypes, further enhancing segmentation performance on old categories. Comprehensive evaluations on two widely used multi-organ segmentation benchmarks demonstrate that our method outperforms current state-of-the-art methods, highlighting its robustness and generalization capabilities.