Small Language Models (SLM) have gained relevance in applications embedded in modern smart devices. Although they have received less attention in the literature concerning large language models (LLMs)-generally implemented in cloud environments- both architectures can aid decision-making to mitigate natural hazards and address other societal challenges. As generalized models, LLMs often struggle to provide context-specific truthful information, specifically in areas that require specialized expertise. To overcome this limitation, we propose a framework that enhances factual knowledge retrieval in SLM through few-shot learning and knowledge graph construction. The proposed approach aims to significantly improve the ability to retrieve truthful, fact-based information while preserving the advantages of accessibility, low computational cost, and energy efficiency inherent to these models. Our experiments, conducted on two natural hazard-related datasets, demonstrate the generalized of our approach. Applying specific metrics, we evaluate not only their hallucination rate but also their information redundancy. Our results demonstrate the potential of SLM to construct knowledge graphs and improve factual knowledge retrieval in specific social contexts.