Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains. For example, in stock markets, the announcement of acquisitions from leading companies may have immediate effects on stock prices and increased uncertainty of the future market due to this past action. This requires the model to take non-linear relationships, instantaneous effects and the past-action dependent uncertainty into account. We name the latter as history-dependent noise. However, previous works do not offer a solution addressing all these problems together. In this paper, we propose a structural equation model, called Rhino, which combines vector auto-regression, deep learning and variational inference to model non-linear relationships with instantaneous effects and flexible history-dependent noise. Theoretically, we prove the structural identifiability for a generalization of Rhino. Our empirical results from extensive synthetic experiments and a real-world benchmark demonstrate better discovery performance compared to relevant baselines, with ablation studies revealing its robustness when the Rhino is misspecified.