Long Answer: A doctor, particularly if it is your primary care physician, will be able to tell if the symptoms of your illness are, or can be, due to alcohol or drug abuse. In either event, your doctor is obligated to keep details of your medical history/condition confidential, in the first instance. So, it is not like the doctor is going to go around and tell everyone about you. Concentrate on getting healthy, and you won't have to worry about what others who might be worried about you are saying.
Short Answer: You have not presented anything which would indicate a worthwhile claim of defamation to pursue.