Hello and hope you are doing well.
The constant coughing could cause muscle strain and chest pain. Sometimes the pleura, the lining of the chest cavity and lungs can get inflamed causing pain with coughing. This should resolve as the infection and inflammation subside. However, if the pain persists or if you develop additional symptoms like fever or cough consult your doctor for an assessment. In the meantime you can take OTC pain medication Ibuprofen. Ensure to take this medication after food to avoid gastritis.
Hope this helped and do keep us posted.