When any part of the body feels itchy, nerves send signals to the brain indicating that histamine -- a chemical released as part of your immune system response to injury or an allergic reaction -- has been released. Itching is a result of this histamine release, and when histamine is released in specific areas like the chin, it can be very irritating.
This itching can be triggered by a variety of things, including dry skin, contact with an allergen or irritation from shaving, or even a reaction to medication (via Healthline). If you suspect one of these is the cause of your itchiness, wash your chin often and use nonirritating lotion to moisturize, avoid contact with any known allergens, or use a mild shampoo to remove any traces of product that may have built up on your face.
However, an itchy chin that occurs in conjunction with coughing could also be a sign of a more serious illness, according to the NHS. If your chin itches when you cough, along with wheezing, tight chest and feeling out of breath, it may be a warning sign of the deadly lung condition asthma. If you experience these symptoms, you should see your doctor immediately. Asthma is more common in children, but it can affect people of any age. Asthma can also be a trigger for other respiratory problems, such as ear infections and gastroesophageal reflux disease.