Pneumonia is one of the leading causes of morbidity and mortality in children. This is especially true in resource poor regions lacking diagnostic facilities, bringing about the need for rapid diagnostic tests for pneumonia. Cough is a common symptom of acute respiratory diseases, including pneumonia, and the sound of cough can be indicative of the pathological variations caused by respiratory infections. As such, in this paper we study objective cough sound evaluation for differentiating between pneumonia and other acute respiratory diseases. We use a dataset of 491 cough sounds from 173 children diagnosed either as having pneumonia or other acute respiratory diseases. We extract features which describe the temporal, spectral, and cepstral characteristics of the cough sound. These features are combined with feature embeddings from a pretrained deep learning network and used to train a multilayer perceptron for classification. The proposed method achieves a sensitivity and specificity of 84% and 73% respectively in differentiating between pneumonia and other acute respiratory diseases using cough sounds alone.