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Nitrogen dioxide (NO$_2$) is a primary atmospheric pollutant and a significant contributor to respiratory morbidity and urban climate-related challenges. While satellite platforms like Sentinel-2 provide global coverage, their native spatial resolution often limits the precision required, fine-grained NO$_2$ assessment. To address this, we propose TinyNina, a resource-efficient Edge-AI framework specifically engineered for sustainable environmental monitoring. TinyNina implements a novel intra-image learning paradigm that leverages the multi-spectral hierarchy of Sentinel-2 as internal training labels, effectively eliminating the dependency on costly and often unavailable external high-resolution reference datasets. The framework incorporates wavelength-specific attention gates and depthwise separable convolutions to preserve pollutant-sensitive spectral features while maintaining an ultra-lightweight footprint of only 51K parameters. Experimental results, validated against 3,276 matched satellite-ground station pairs, demonstrate that TinyNina achieves a state-of-the-art Mean Absolute Error (MAE) of 7.4 $\mu$g/m$^3$. This performance represents a 95% reduction in computational overhead and 47$\times$ faster inference compared to high-capacity models such as EDSR and RCAN. By prioritizing task-specific utility and architectural efficiency, TinyNina provides a scalable, low-latency solution for real-time air quality monitoring in smart city infrastructures.