While Approximate Computing (AxC) is a promising technique to trade off accuracy for energy efficiency, one fundamental challenge is the lack of accurate and informative error models of AxC applications. In this work, we propose PreAxC, a novel error modeling and prediction flow for AxC designs. Instead of using simple error statistics as in existing work, we use error distribution for AxC circuit error analysis with input awareness. We propose Graph Neural Network (GNN) based methods to predict the error distribution of AxC programs, which are represented as Data Flow Graphs (DFGs). We propose two approaches: model- free and model-based, where the former directly predicts the error distribution histogram, and the latter models the distribution using Gaussian Mixture Model (GMM) and predicts the GMM parameters. Experiment results demonstrate that our approaches can outperform existing error statistics and can successfully predict the error distribution, especially the model-free approach, even for completely unseen graphs (representing new AxC programs) during training.