Image-to-image translation has emerged as a powerful technique in medical imaging, enabling tasks such as image denoising and cross-modality conversion. However, it suffers from limitations in handling out-of-distribution samples without causing performance degradation. To address this limitation, we propose a novel Test-Time Adaptation (TTA) framework that dynamically adjusts the translation process based on the characteristics of each test sample. Our method introduces a Reconstruction Module to quantify the domain shift and a Dynamic Adaptation Block that selectively modifies the internal features of a pretrained translation model to mitigate the shift without compromising the performance on in-distribution samples that do not require adaptation. We evaluate our approach on two medical image-to-image translation tasks: low-dose CT denoising and T1 to T2 MRI translation, showing consistent improvements over both the baseline translation model without TTA and prior TTA methods. Our analysis highlights the limitations of the state-of-the-art that uniformly apply the adaptation to both out-of-distribution and in-distribution samples, demonstrating that dynamic, sample-specific adjustment offers a promising path to improve model resilience in real-world scenarios. The code is available at: https://github.com/Sample-Aware-TTA/Code.