In this paper, we address computer-aided speech diagnosis by designing a method for the automated detection of Polish sibilants in preschool children. Our database was recorded from 47 children aged four to seven using a 15-channel data acquisition device. We propose a modified YAMNet architecture to classify short speech segments from the main channel into four classes. The segments are represented by a dedicated acoustic image based on filter-bank energies and their derivatives. We use a set of time-series data augmentation procedures over the data from all microphones to improve training. With the segment classification results, we determine a frame-wise speech segmentation to extract sibilants. Our segment classification model yields overall accuracy of 87.9%, with the sibilant classification recall and precision at 92.3% and 87.7%, respectively. The sibilant segmentation accuracy reaches 96.2% with an F1 score of 73.5%.