Neonatal pain assessment in clinical environments is challenging as it is discontinuous and biased. Facial/body occlusion can occur in such settings due to clinical condition, developmental delays, prone position, or other external factors. In such cases, crying sound can be used to effectively assess neonatal pain. In this paper, we investigate the use of a novel CNN architecture (N-CNN) along with other CNN architectures (VGG16 and ResNet50) for assessing pain from crying sounds of neonates. The experimental results demonstrate that using our novel N-CNN for assessing pain from the sounds of neonates has a strong clinical potential and provides a viable alternative to the current assessment practice.