The Competitive Influence Maximization (CIM) problem involves multiple entities competing for influence in online social networks (OSNs). While Deep Reinforcement Learning (DRL) has shown promise, existing methods often assume users' opinions are binary and ignore their behavior and prior knowledge. We propose DRIM, a multi-dimensional uncertainty-aware DRL-based CIM framework that leverages Subjective Logic (SL) to model uncertainty in user opinions, preferences, and DRL decision-making. DRIM introduces an Uncertainty-based Opinion Model (UOM) for a more realistic representation of user uncertainty and optimizes seed selection for propagating true information while countering false information. In addition, it quantifies uncertainty in balancing exploration and exploitation. Results show that UOM significantly enhances true information spread and maintains influence against advanced false information strategies. DRIM-based CIM schemes outperform state-of-the-art methods by up to 57% and 88% in influence while being up to 48% and 77% faster. Sensitivity analysis indicates that higher network observability and greater information propagation boost performance, while high network activity mitigates the effect of users' initial biases.