Background: Breast and thyroid cancers pose an increasing public-health burden. Ultrasound imaging is a cost-effective, real-time modality for lesion detection and segmentation, yet suffers from speckle noise, overlapping structures, and weak global-local feature interactions. Existing networks struggle to reconcile high-level semantics with low-level spatial details. We aim to develop a segmentation framework that bridges the semantic gap between global context and local detail in noisy ultrasound images. Methods: We propose UESA-Net, a U-shaped network with multidirectional shrinkage attention. The encoder-decoder architecture captures long-range dependencies and fine-grained structures of lesions. Within each encoding block, attention modules operate along horizontal, vertical, and depth directions to exploit spatial details, while a shrinkage (threshold) strategy integrates prior knowledge and local features. The decoder mirrors the encoder but applies a pairwise shrinkage mechanism, combining prior low-level physical cues with corresponding encoder features to enhance context modeling. Results: On two public datasets - TN3K (3493 images) and BUSI (780 images) - UESA-Net achieved state-of-the-art performance with intersection-over-union (IoU) scores of 0.8487 and 0.6495, respectively. Conclusions: UESA-Net effectively aggregates multidirectional spatial information and prior knowledge to improve robustness and accuracy in breast and thyroid ultrasound segmentation, demonstrating superior performance to existing methods on multiple benchmarks.