Recent breakthroughs in Transformer-based large models, have driven widespread tasks, yet their reliance on centralized cloud deployment raises significant privacy risks due to sensitive data exposure. While edge-based collaborative inference offers a privacy-preserving alternative, existing methods face critical limitations: static model partitioning cannot adapt to dynamic edge resource fluctuations, and rigid multi-head attention handling overlooks semantic-critical prioritization and parallelism. We propose EdgeFormer, a latency-aware framework for distributed Transformer inference in resource-constrained edge networks. EdgeFormer dynamically allocates model blocks across devices via efficiency-storage trade-off optimization and introduces collaborative Multi-Head Attention (cMHA), which distributes semantic-critical attention heads across devices while pruning redundant ones under real-time constraints. We further develop LiScore, a composite metric integrating attention diversity and latency costs, alongside a similarity-based retrieval method to reduce recomputation overhead. Extensive experiments demonstrate that EdgeFormer achieves up to 2.01 \\times inference acceleration over state-of-the-art baselines with \\leq1.06% accuracy loss, maintaining robustness under varying edge conditions.