Yes, Benadryl (an antihistamine) can help you.
Here's a simplistic explanation, believe me I learned this when my son was little and he developed asthma. I ignored his doctor, who prescribed horrible drugs that were making him sicker, and treated his allergies instead. Try to find the best antihistamine for you by experimenting.
Think of it as an interior drip (definitely from allergies, especially animal dander from pets in the home) that goes down you throat into your bronchial tubes, especially at night. That causes the coughing. If you dry it up with an antihistamine you won't have all the cough.
Good luck and hope this helps you.