Search engines are vital for online e-commerce but often struggle with long, detailed queries. We introduce Search Swarm, a novel multi-agent system designed to improve search engine navigation on platforms like Amazon by accurately locating relevant products based on user instructions. Search Swarm employs multiple large language model (LLM) agents, each with a specific role: query planner, searcher, critic, and attribute selector. These agents collaborate to generate search queries, evaluate results, and identify the best product options tailored to users' needs. Our framework outperforms existing methods like ReAct and Reflexion in the WebShop environment, achieving a reward score of 62.64, compared to scores of 54.1, 59.8, 61.5, and 58.2 for other approaches. Furthermore, in a comparison with a basic rule-based method on Amazon, Search Swarm achieved a score 38.71 points higher and a 41\% greater success rate, demonstrating its superior ability to provide relevant product matches over traditional search engines.