Channel estimation is crucial in 5G communication networks for optimizing transmission parameters and ensuring reliable, high-speed communication. However, the use of multiple-input and multiple-output (MIMO) and millimeter-wave (mmWave) in 5G networks presents challenges in achieving accurate estimation under strict latency requirements on resource-limited hardware platforms. To address these challenges, we propose SwiftChannel, an algorithm-hardware co-design framework that integrates a hardware-friendly deep learning-based channel estimator with a dedicated accelerator. Our approach employs a convolutional neural network enhanced with a parameter-free attention mechanism, which effectively reconstructs full-resolution spatial-frequency domain channel matrices from low-resolution least squares (LS) estimates. We further develop a multi-stage model compression pipeline combining knowledge distillation, convolution re-parameterization, and quantization-aware training, resulting in substantial model size reduction with negligible accuracy loss. The hardware accelerator, implementing the compressed model and the LS estimator on FPGA platforms using High-level Synthesis (HLS), features a fine-grained pipeline architecture and optimized dataflow strategies. Tested on a Zynq UltraScale+ RFSoC, the accelerator achieves sub-millisecond latency, providing up to 24x speed-up and over 33x improvement in energy efficiency compared to GPU-based solutions. Extensive evaluations demonstrate that the proposed design generalizes not only across various noise levels and user mobilities, but also to a variety of unseen channel profiles, outperforming state-of-the-art baselines. By unifying algorithmic innovation with hardware-aware design, our work presents a future-proof channel estimation solution for 5G MIMO systems.