We present Look-Back and Look-Ahead Adaptive Model Predictive Control (LLA-MPC), a real-time adaptive control framework for autonomous racing that addresses the challenge of rapidly changing tire-surface interactions. Unlike existing approaches requiring substantial data collection or offline training, LLA-MPC employs a model bank for immediate adaptation without a learning period. It integrates two key mechanisms: a look-back window that evaluates recent vehicle behavior to select the most accurate model and a look-ahead horizon that optimizes trajectory planning based on the identified dynamics. The selected model and estimated friction coefficient are then incorporated into a trajectory planner to optimize reference paths in real-time. Experiments across diverse racing scenarios demonstrate that LLA-MPC outperforms state-of-the-art methods in adaptation speed and handling, even during sudden friction transitions. Its learningfree, computationally efficient design enables rapid adaptation, making it ideal for high-speed autonomous racing in multisurface environments.