Deep learning has made significant progress in natural image segmentation but faces challenges in medical imaging due to the limited availability of annotated data. Few-shot learning offers a solution by enabling segmentation with only a few labeled samples, yet generalization remains a challenge when data is scarce. In this work, we investigate the potential of the Segment Anything Model (SAM), a foundation model trained on over one billion annotated images, for few-shot medical image segmentation. However, SAM faces two key challenges: (1) the domain gap between natural and medical images, leading to suboptimal performance, and (2) prompt dependency, as SAM requires user-defined prompts, limiting automation. To address these issues, we propose a novel framework, named AM-SAM, that adapts SAM for few-shot medical image segmentation. Our approach introduces a medical image-specific augmentation strategy and a dual-encoder architecture to bridge the domain gap. Additionally, we develop an automated dual-prompt mechanism to eliminate prompt dependency, generating point and mask prompts from support images. Extensive experiments show that AM-SAM outperforms existing approaches by up to 3.8% on ABD-MRI and 4.0% on ABD-30 in terms of dice score metric.