Reinforcement Learning (RL) is increasingly being applied to complex decision-making tasks such as financial trading. However, designing effective reward functions remains a significant challenge. Traditional static reward functions often fail to adapt to dynamic environments, leading to inefficiencies in learning. This paper presents a novel approach, called Self-Rewarding Deep Reinforcement Learning (SRDRL), which integrates a self-rewarding network within the RL framework. The SRDRL mechanism operates in two primary phases: First, supervised learning techniques are used to learn from expert knowledge by employing advanced time-series feature extraction models, including TimesNet and WFTNet. This step refines the self-rewarding network parameters by comparing predicted rewards with expert-labeled rewards, which are based on metrics such as Min-Max, Sharpe Ratio, and Return. In the second phase, the model selects the higher value between the expert-labeled and predicted rewards as the RL reward, storing it in the replay buffer. This combination of expert knowledge and predicted rewards enhances the performance of trading strategies. The proposed implementation, called Self-Rewarding Double DQN (SRDDQN), demonstrates that the self-rewarding mechanism improves learning and optimizes trading decisions. Experiments conducted on datasets including DJI, IXIC, and SP500 show that SRDDQN achieves a cumulative return of 1124.23% on the IXIC dataset, significantly outperforming the next best method, Fire (DQN-HER), which achieved 51.87%. SRDDQN also enhances the stability and efficiency of trading strategies, providing notable improvements over traditional RL methods. The integration of a self-rewarding mechanism within RL addresses a critical limitation in reward function design and offers a scalable, adaptable solution for complex, dynamic trading environments.