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To reduce doctors' workload, deep-learning-based automatic medical report generation has recently attracted more and more research efforts, where attention mechanisms and reinforcement learning are integrated with the classic encoder-decoder architecture to enhance the performance of deep models. However, these state-of-the-art solutions mainly suffer from two shortcomings: (i) their attention mechanisms cannot utilize high-order feature interactions, and (ii) due to the use of TF-IDF-based reward functions, these methods are fragile with generating repeated terms. Therefore, in this work, we propose a reinforced medical report generation solution with x-linear attention and repetition penalty mechanisms (ReMRG-XR) to overcome these problems. Specifically, x-linear attention modules are used to explore high-order feature interactions and achieve multi-modal reasoning, while repetition penalty is used to apply penalties to repeated terms during the model's training process. Extensive experimental studies have been conducted on two public datasets, and the results show that ReMRG-XR greatly outperforms the state-of-the-art baselines in terms of all metrics.