Accurate and timely differentiation of pulmonary diseases — including COVID-19, community-acquired pneumonia, and tuberculosis — from chest radiographs remains a clinically significant challenge, as these conditions frequently present with overlapping radiological manifestations that impede both manual and automated diagnosis. Existing deep learning approaches predominantly rely on either convolutional neural networks, which excel at local texture and boundary extraction but lack global contextual reasoning, or Vision Transformers, which model long-range dependencies but require substantially larger datasets and extended training resources. This study proposes a novel hybrid architecture that systematically addresses these complementary limitations through three integrated components. First, a pretrained EfficientNet-B3 backbone extracts hierarchical local features from chest radiographs at 224×224 resolution. Second, a proposed Dynamic Dual Attention module (DyDA) applies channel and spatial attention pathways in parallel and combines their outputs via a pair of input-dependent learnable gates α and β, constrained by softmax normalization such that α + β = 1, enabling the model to dynamically emphasize either channel-wise or spatially-localized features according to the pathological content of each individual image — in contrast to CBAM's fixed sequential formulation and DANet's globally-constant scalar weighting. Third, a Swin Transformer captures shifted-window global context from the attended feature representations, and the resulting CNN and Transformer feature vectors are fused through a concatenation layer before a fully connected classification head with dropout regularization. The proposed system is evaluated on a multi-source dataset combining the COVID-19 Radiography Database, the Kaggle Chest X-Ray Pneumonia dataset, and the Montgomery County and Shenzhen tuberculosis collections, employing five-fold stratified cross-validation with CLAHE preprocessing and domain-appropriate augmentation. Comprehensive ablation experiments isolate the contribution of each architectural component across backbone-only, CBAM-augmented, DyDA-without-Swin, and full-model configurations. Grad-CAM saliency maps are generated to confirm that model predictions align with clinically relevant radiological regions, supporting interpretability for potential clinical decision support applications.