Medical question answering systems face deployment challenges including hallucinations, bias, computational demands, privacy concerns, and the need for specialized expertise across diverse domains. Here, we present SOLVE-Med, a multi-agent architecture combining domain-specialized small language models for complex medical queries. The system employs a Router Agent for dynamic specialist selection, ten specialized models (1B parameters each) fine-tuned on specific medical domains, and an Orchestrator Agent that synthesizes responses. Evaluated on Italian medical forum data across ten specialties, SOLVE-Med achieves superior performance with ROUGE-1 of 0.301 and BERTScore F1 of 0.697, outperforming standalone models up to 14B parameters while enabling local deployment. Our code is publicly available on GitHub: https://github.com/PRAISELab-PicusLab/SOLVE-Med.