5G is bringing new use cases to the forefront, one of the most prominent being machine learning empowered health care. Since respiratory infections are one of the notable modern medical concerns and coughs being a common symptom of this, a system for recognizing and diagnosing infections based on raw cough data would have a multitude of beneficial research and medical applications. In the literature, machine learning has been successfully used to detect cough events in controlled environments. In this work, we present a novel system that utilizes Convolutional Neural Networks (CNNs) to detect cough within environment audio and diagnose three potential illnesses (i.e., Bronchitis, Bronchiolitis, and Pertussis) based on their unique cough audio features. Our detection model achieves an accuracy of 90.17% and a specificity of 89.73%, whereas the diagnosis model achieves an accuracy of about 94.74% and an F1 score of 93.73%. These results clearly show that our system is successfully able to detect and separate cough events from background noise. Moreover, our single diagnosis model is capable of distinguishing between different illnesses without the need of separate models.