The interest in automated analysis and classification of cough sounds has increased in recent years, partly due to the worldwide COVID19 pandemic. To train such classification models, a large dataset of cough sounds is needed, however, it remains challenging to find such datasets of cough sounds that have expert-labelled diagnoses of cough types. Data augmentation techniques have been used to train machine learning models given such limited data. Furthermore, augmentation ensures that trained models are invariant to natural transformations of the data, measured from real environments/surroundings. This paper presents a method for classifying wet and dry coughs using a ResNet18 convolutional neural network model. Several forms of spectral data augmentation are investigated including many traditional audio data augmentation methods. A novel form of audio data augmentation is leveraged, where coughs are augmented with varying levels of reverberation and Gaussian noise, during model training. The study found that using a combination of reverb and noise augmentation provided greater improvement than either form of augmentation alone, or traditional augmentations as well, leading to an accuracy of 95%. Use of such a model that has been trained on both reverb- and noise-augmented data is recommended when classifying audio recordings, such as cough sounds, from natural environments outside of laboratory conditions.