This study introduces LoGoSAM, a novel framework designed for one-shot medical image segmentation by leveraging the capabilities of Prototypical Networks with Visual Prompting. Although recent research has explored various strategies to improve one-shot segmentation in medical imaging, most approaches rely heavily on convolutional architectures or pretrained transformer-based encoders for extracting feature similarity. LoGoSAM enhances this technique by introducing an encoding function that simultaneously captures both local patterns and global dependencies within a medical image. This dual representation facilitates the extraction of more representative prototypes, which are crucial for generating robust visual prompts, as bounding boxes or similarity maps. These prompts enable subsequent refinement using the Segment Anything Model (SAM), significantly boosting segmentation performance. Experimental results demonstrate the effectiveness of LoGoSAM in advancing one-shot segmentation for complex medical imaging tasks.