Pneumonia remains a leading cause of pediatric mortality, necessitating rapid and accurate screening via Chest X-Rays (CXR) to facilitate early clinical intervention. However, the subtle and overlapping pathological features in pediatric scans often exacerbate diagnostic workloads and inter-observer variability among radiologists. While deep learning offers promising automated solutions, deploying architectures on constrained medical datasets frequently results in severe overfitting and catastrophic forgetting. To address this, we propose an optimized, computationally efficient automated diagnostic framework utilizing a frozen-backbone ResNet18 architecture. Employing a strict transfer learning paradigm, we froze the deep convolutional feature extractors while fine-tuning the classification head, further mitigating dataset imbalances through dynamic class-weight penalties and robust spatial augmentations. Crucially, the framework integrates a dynamic learning rate scheduler coupled with a custom "Restore Best Weights" algorithm, preventing model degradation by automatically halting training and retrieving the most clinically viable weights prior to validation loss divergence. Evaluated on a comprehensive pediatric CXR dataset, the optimized model achieved a robust overall validation accuracy of 86.54%. More importantly for primary medical screening applications, the model demonstrated an outstanding sensitivity (recall) of 91.79%, successfully minimizing critical false negatives, alongside a precision of 87.10%, a specificity of 77.35%, and an overall F1-score of 89.39%. By maximizing diagnostic sensitivity and maintaining stable training convergence without massive computational overhead, this AI-driven approach provides a highly reliable, scalable second-reader tool for pediatric radiologists, significantly streamlining screening workflows and supporting rapid, life-saving clinical decisions.