Code comments provide essential documentation for software understanding, yet their automated classification remains challenging due to severe class imbalance and computational constraints. This paper proposes TraCC (Transformer-aided Code Comment Classification), a solution that combines CodeBERT teacher models with TinyBERT student models through knowledge distillation. We address class imbalance using LLM-based data augmentation with Google Gemini, asymmetric focal loss, and per-label dynamic threshold optimization. Evaluated on an augmented dataset derived from 14,875 comments across Java, Python, and Pharo, our distilled TinyBERT models achieve an average F1 score of 0.671 with superior computational efficiency: 481 GFLOPs and 0.565 seconds runtime. The approach demonstrates 23-63% improvements on minority classes while achieving 88% parameter reduction compared to teacher models.