To facilitate early detection of breast cancer, there is a need to develop short-term risk prediction schemes that can prescribe personalized/individualized screening mammography regimens for women. In this study, we propose a new deep learning architecture called TRINet that implements time-decay attention to focus on recent mammographic screenings, as current models do not account for the relevance of newer images. We integrate radiomic features with an Attention-based Multiple Instance Learning (AMIL) framework to weigh and combine multiple views for better risk estimation. In addition, we introduce a continual learning approach with a new label assignment strategy based on bilateral asymmetry to make the model more adaptable to asymmetrical cancer indicators. Finally, we add a time-embedded additive hazard layer to perform dynamic, multi-year risk forecasting based on individualized screening intervals. We used two public datasets, namely 8,528 patients from the American EMBED dataset and 8,723 patients from the Swedish CSAW dataset in our experiments. Evaluation results on the EMBED test set show that our approach significantly outperforms state-of-the-art models, achieving AUC scores of 0.851, 0.811, 0.796, 0.793, and 0.789 across 1-, 2-, to 5-year intervals, respectively. Our results underscore the importance of integrating temporal attention, radiomic features, time embeddings, bilateral asymmetry, and continual learning strategies, providing a more adaptive and precise tool for short-term breast cancer risk prediction.