The rise of "bedroom producers" has democratized music creation, while challenging producers to objectively evaluate their work. To address this, we present AI TrackMate, an LLM-based music chatbot designed to provide constructive feedback on music productions. By combining LLMs' inherent musical knowledge with direct audio track analysis, AI TrackMate offers production-specific insights, distinguishing it from text-only approaches. Our framework integrates a Music Analysis Module, an LLM-Readable Music Report, and Music Production-Oriented Feedback Instruction, creating a plug-and-play, training-free system compatible with various LLMs and adaptable to future advancements. We demonstrate AI TrackMate's capabilities through an interactive web interface and present findings from a pilot study with a music producer. By bridging AI capabilities with the needs of independent producers, AI TrackMate offers on-demand analytical feedback, potentially supporting the creative process and skill development in music production. This system addresses the growing demand for objective self-assessment tools in the evolving landscape of independent music production.