Ultrasound imaging is the primary diagnostic modality for detecting Gallbladder diseases due to its non-invasive nature, affordability, and wide accessibility. However, the low resolution and speckle noise inherent to ultrasound images hinder diagnostic reliability, prompting the use of large convolutional neural networks that are difficult to deploy in routine clinical settings. In this work, we propose CortiNet, a lightweight, cortical-inspired dual-stream neural architecture for gallbladder disease diagnosis that integrates physically interpretable multi-scale signal decomposition with perception-driven feature learning. Inspired by parallel processing pathways in the human visual cortex, CortiNet explicitly separates low-frequency structural information from high-frequency perceptual details and processes them through specialized encoding streams. By operating directly on structured, frequency-selective representations rather than raw pixel intensities, the architecture embeds strong physics-based inductive bias, enabling efficient feature learning with a significantly reduced parameter footprint. A late-stage cortical-style fusion mechanism integrates complementary structural and textural cues while preserving computational efficiency. Additionally, we propose a structure-aware explainability framework wherein gradient-weighted class activation mapping is only applied to the structural branch of the proposed CortiNet architecture. This choice allows the model to only focus on the structural features, making it robust against speckle noise. We evaluate CortiNet on 10,692 expert-annotated images spanning nine clinically relevant gallbladder disease categories. Experimental results demonstrate that CortiNet achieves high diagnostic accuracy (98.74%) with only a fraction of the parameters required by conventional deep convolutional models.