The prototypical network effectively classifies skin diseases in few-shot learning but faces challenges with prototype accuracy due to limited data and insufficient long-term knowledge retention, affecting generalization to new classes. However, the prototypical network faces challenges such as inaccurate prototype estimations due to limited data and insufficient long-term knowledge retention, affecting its generalization to new classes. This study introduces CGProNet (Continual Graph-based Prototypical Networks for Few-Shot Skin Disease Classification) to address these issues and improve the accuracy of uncommon skin disease identification. CGProNet employs prototype network-based support samples and considers their interdependencies while transferring knowledge across tasks. It uses Convolutional CNNs to generate initial features, graph-based methods to capture relational information, and gated recurrent units (GRUs) to preserve graph-aggregated features. CGProNet achieves 80.5% accuracy on the ISIC-2018, 86.03% on the Derm7pt, and 92.51% on the SD-198 datasets in 5-shot learning scenarios, proving effective for skin disease classification with limited data.