Accurate classification of breast ultrasound images into benign, malignant, and normal categories is a critical clinical task complicated by speckle noise, acoustic shadowing, and inter-class visual ambiguity. Existing deep learning methods rely on single-stream architectures with generic augmentation that ignores ultrasound acquisition physics, and no prior method dedicates a stream to the lesion boundary features identified as the most diagnostically significant visual cue. We propose HADS-Net, a Hybrid Attention-Augmented Dual-Stream Network exploiting global texture and local boundary cues through two parallel pathways. Stream 1 applies physics-informed augmentation simulating speckle noise, acoustic shadowing, and gain variation before extracting features via pretrained EfficientNet-B3 projected to 512 dimensions. Stream 2 extracts Sobel edge maps processed by a lightweight CNN projected to the same 512-dimensional space. A cross-attention fusion module allows the texture stream to selectively query boundary features, producing a jointly optimised representation classified by an MLP trained with adaptive class-weighted focal loss. Five-fold stratified cross-validation with cosine annealing over 50 epochs is used, with the globally best checkpoint selected by lowest validation loss evaluated on a held-out test set. On the BUSI dataset, HADS-Net achieves 96.58% accuracy, macro ROC-AUC of 0.9978, macro F1 of 0.9654, and per-class F1-scores of 0.970, 0.951, and 0.976 for benign, malignant, and normal. No malignant lesion is misclassified as normal. These results confirm that modality-specific augmentation with cross-modal attention fusion is an effective strategy for ultrasound-based breast cancer diagnosis.