This work aims to investigate semantic communication in high-speed mobile Internet of vehicles (IoV) environments, with a focus on the spectrum sharing between vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications. We specifically address spectrum scarcity and network traffic and then propose a semantic-aware spectrum sharing algorithm (SSS) based on the deep reinforcement learning (DRL) soft actor-critic (SAC) approach. Firstly, we delve into the extraction of semantic information. Secondly, we redefine metrics for semantic information in V2V and V2I spectrum sharing in IoV environments, introducing high-speed semantic spectrum efficiency (HSSE) and semantic transmission rate (HSR). Finally, we employ the SAC algorithm for decision optimization in V2V and V2I spectrum sharing based on semantic information. This optimization encompasses the optimal link of V2V and V2I sharing strategies, the transmission power for vehicles sending semantic information and the length of transmitted semantic symbols, aiming at maximizing HSSE of V2I and enhancing success rate of effective semantic information transmission (SRS) of V2V. Experimental results demonstrate that the SSS algorithm outperforms other baseline algorithms, including other traditional-communication-based spectrum sharing algorithms and spectrum sharing algorithm using other reinforcement learning approaches. The SSS algorithm exhibits a 15% increase in HSSE and approximately a 7% increase in SRS.