Computed tomography (CT) is important in clinical diagnosis, but acquiring high-resolution (HR) CT is constrained by radiation exposure risks. While deep learning-based super-resolution (SR) methods have shown promise for reconstructing HR CT from low-resolution (LR) inputs, supervised approaches require paired datasets that are often unavailable. Zero-shot methods address this limitation by operating on single LR inputs; however, they frequently fail to recover fine structural details due to limited LR information within individual volumes. To overcome these limitations, we propose a novel zero-shot 3D CT SR framework that integrates diffusion-based upsampled 2D projection priors into the 3D reconstruction process. Specifically, our framework consists of two stages: (1) LR CT projection SR, training a diffusion model on abundant X-ray data to upsample LR projections, thereby enhancing the scarce information inherent in the LR inputs. (2) 3D CT volume reconstruction, using 3D Gaussian splatting with our novel Negative Alpha Blending (NAB-GS), which models positive and negative Gaussian densities to learn signed residuals between diffusion-generated HR and upsampled LR projections. Our framework demonstrates superior quantitative and qualitative performance on two public datasets, and expert evaluations present the framework's clinical potential at 4x.