Multi-label image classification in dynamic environments is a problem that poses significant challenges. Previous studies have primarily focused on scenarios such as Domain Incremental Learning and Class Incremental Learning, which do not fully capture the complexity of real-world applications. In this paper, we study the problem of classification of medical imaging in the scenario termed New Instances and New Classes, which combines the challenges of both new class arrivals and domain shifts in a single framework. Unlike traditional scenarios, it reflects the realistic nature of CL in domains such as medical imaging, where updates may introduce both new classes and changes in domain characteristics. To address the unique challenges posed by this complex scenario, we introduce a novel approach called Pseudo-Label Replay. This method aims to mitigate forgetting while adapting to new classes and domain shifts by combining the advantages of the Replay and Pseudo-Label methods and solving their limitations in the proposed scenario. We evaluate our proposed approach on a challenging benchmark consisting of two datasets, seven tasks, and nineteen classes, modeling a realistic Continual Learning scenario. Our experimental findings demonstrate the effectiveness of Pseudo-Label Replay in addressing the challenges posed by the complex scenario proposed. Our method surpasses existing approaches, exhibiting superior performance while showing minimal forgetting.