Sparse-view computed tomography (CT) reconstruction suffers from streak artifacts and loss of fine detail after filtered back-projection (FBP). To alleviate these issues, we propose a self-supervised dual-domain swin transformer (DuDoSwin) that performs sinogram angular super-resolution and image-domain refinement, connected via a differentiable FBP bridge for end-to-end optimization. On the AAPM Low-Dose CT dataset, DuDoSwin achieves superior reconstruction quality and perceptual fidelity compared to existing learning-based and interpolation-based methods, improving quantitative (PSNR/SSIM/LPIPS) metrics under severe angular undersampling (4×, 8×, 16×). By jointly modeling projection and image domains, the proposed dual-domain design restores sharp anatomical structures and enhances perceptual quality, contributing to higher-quality low-dose CT reconstruction. The implementation is available at https://github.com/bipin-y-lab/DuDoSwin.