Finding events actively discussed locally or globally is a significant problem when mining social media data streams. Identifying such events can serve as an early warning system in an event such as an accident, a protest, an election, or other breaking news. However, with the massive volume of social media feeds streaming, early detection of such events is inherently complex. Despite the advances in social media event detection, existing methods often struggle with the dynamic nature of social media, the volume and velocity of data, and the ambiguity in user-generated content. On the contrary, several relational aspects are present in social media that, if suitably handled and exploited, can improve detection performance. To mitigate these challenges, we propose "DistilBERT-GNN," an incremental event detection framework that leverages DistilBERT and Graph Neural Networks (GNNs). By integrating DistilBERT's real-time contextual understanding with GNNs' ability to capture evolving relationships in social media networks, our framework aims to detect and track events as they emerge and evolve. We assess the effectiveness of our approach through comparative analysis against various state-of-the-art event detection methods on a real-world Twitter dataset. Our experimental result demonstrates that DistilBERT-GNN outperforms the baselines with NMI, AMI, and ARI metrics by 0.72, 0.53, and 0.24, respectively.