Contextual clinical reasoning demands robust inference grounded in complex, heterogeneous clinical records. While state-of-the-art fine-tuning, in-context learning (ICL), and retrieval-augmented generation (RAG) enable knowledge exposure, they often fall short of genuine contextual internalization: dynamically adjusting a model's internal representations to the subtle nuances of individual cases at inference time. To address this, we propose Dual-Stream Calibration (DSC), a test-time training framework that transcends superficial knowledge exposure to achieve deep internalization during inference. DSC facilitates input internalization by synergistically aligning two calibration streams. Unlike passive context exposure, the Semantic Calibration Stream enforces a deliberative reflection on core evidence, internalizing semantic anchors by minimizing entropy to stabilize generative trajectories. Simultaneously, the Structural Calibration Stream assimilates latent inferential dependencies through an iterative meta-learning objective. By training on specialized support sets at test-time, this stream enables the model to bridge the gap between external evidence and internal logic, synthesizing fragmented data into a coherent response. Our approach shifts the reasoning paradigm from passive attention-based matching to an active refinement of the latent inferential space. Validated against thirteen clinical datasets, DSC demonstrates superiority across three distinct task paradigms, consistently outstripping state-of-the-art baselines ranging from training-dependent models to test-time learning frameworks.