Controlling the shape of deformable linear objects using robots and constraints provided by environmental fixtures has diverse industrial applications. In order to establish robust contacts with these fixtures, accurate estimation of the contact state is essential for preventing and rectifying potential anomalies. However, this task is challenging due to the small sizes of fixtures, the requirement for real-time performances, and the infinite degrees of freedom of the deformable linear objects. In this paper, we propose a real-time approach for estimating both contact establishment and subsequent changes by leveraging the dependency between the applied and detected contact force on the deformable linear objects. We seamlessly integrate this method into the robot control loop and achieve an adaptive shape control framework which avoids, detects and corrects anomalies automatically. Real-world experiments validate the robustness and effectiveness of our contact estimation approach across various scenarios, significantly increasing the success rate of shape control processes.