There are several potential causes of arm pain that may be associated with coughing. Some common causes include:

1. Muscular strain: Coughing can put a lot of strain on the muscles of the chest and arms, especially if the cough is particularly severe or persistent. This can lead to muscle pain and discomfort.
2. Nerve irritation: The nerves that supply the arm and chest muscles can become irritated or compressed during a cough, leading to pain in the arm.
3. Chest injury: If the arm pain is accompanied by chest pain or discomfort, it is possible that there is an injury or underlying condition in the chest that is causing the cough and associated arm pain. This could include conditions such as pneumonia or a rib fracture.
4. Heart problems: In rare cases, arm pain that occurs during coughing may be a sign of a heart problem, such as angina or a heart attack. This is more likely if the arm pain is accompanied by other symptoms, such as chest pain, shortness of breath, or nausea.

To determine the cause of arm pain that occurs during coughing, it is important to seek medical attention. A healthcare provider will take a thorough medical history and perform a physical examination to help determine the underlying cause of the arm pain and the best course of treatment.

In summary, arm pain that occurs during coughing can have a variety of causes, including muscular strain, nerve irritation, chest injury, or heart problems. It is important to seek medical attention in order to determine the underlying cause and receive appropriate treatment.