This paper studies the allocation of shared resources between vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) links in vehicle-to-everything (V2X) communications. In existing algorithms, dynamic vehicular environments and quantization of continuous power become the bottlenecks for providing an effective and timely resource allocation policy. In this paper, we develop two algorithms to deal with these difficulties. First, we propose a deep reinforcement learning (DRL)-based resource allocation algorithm to improve the performance of both V2I and V2V links. Specifically, the algorithm uses deep Q-network (DQN) to solve the sub-band assignment and deep deterministic policy-gradient (DDPG) to solve the continuous power allocation problem. Second, we propose a meta-based DRL algorithm to enhance the fast adaptability of the resource allocation policy in the dynamic environment. Numerical results demonstrate that the proposed DRL-based algorithm can significantly improve the performance compared to the DQN-based algorithm that quantizes continuous power. In addition, the proposed meta-based DRL algorithm can achieve the required fast adaptation in the new environment with limited experiences.