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Predicting the interaction between a compound and a target is crucial for rapid drug repurposing. Deep learning has been successfully applied in drug-target affinity (DTA) problem. However, previous deep learning-based methods ignore modeling the direct interactions between drug and protein residues. This would lead to inaccurate learning of target representation which may change due to the drug binding effects. In addition, previous DTA methods learn protein representation solely based on a small number of protein sequences in DTA datasets while neglecting the use of proteins outside of the DTA datasets. We propose GEFA (Graph Early Fusion Affinity), a novel graph-in-graph neural network with attention mechanism to address the changes in target representation because of the binding effects. Specifically, a drug is modeled as a graph of atoms, which then serves as a node in a larger graph of residues-drug complex. The resulting model is an expressive deep nested graph neural network. We also use pre-trained protein representation powered by the recent effort of learning contextualized protein representation. The experiments are conducted under different settings to evaluate scenarios such as novel drugs or targets. The results demonstrate the effectiveness of the pre-trained protein embedding and the advantages our GEFA in modeling the nested graph for drug-target interaction.