The present work proposes a deep-learning-based approach for the classification of COVID-19 coughs from non-COVID-19 coughs and that can be used as a low-resource-based tool for early detection of the onset of such respiratory diseases. The proposed system uses the ResNet-50 architecture, a popularly known Convolutional Neural Network (CNN) for image recognition tasks, fed with the log-Mel spectrums of the audio data to discriminate between the two types of coughs. For the training and validation of the proposed deep learning model, this work utilizes the Track-1 dataset provided by the DiCOVA Challenge 2021 organizers. Additionally, to increase the number of COVID-positive samples and to enhance variability in the training data, it has also utilized a large open-source database of COVID-19 coughs collected by the EPFL CoughVid team. Our developed model has achieved an average validation AUC of 98.88%. Also, applying this model on the Blind Test Set released by the DiCOVA Challenge, the system has achieved a Test AUC of 75.91%, Test Specificity of 62.50%, and Test Sensitivity of 80.49%. Consequently, this submission has secured 16th position in the DiCOVA Challenge 2021 leader-board.