I certainly don't agree you did the right thing by not telling a doctor you are a recovering alcoholic...imagine if something went wrong and you had health problems of some sort and your doctor is now trying to make a diagnosis given only some of the information...really is old behaviour IMO
As for alcoholic, i see a CBT counselor whois recovered 24 years and has worked in the most well known 12 step rehab centres in the UK...he considers alcoholic a label too so he, and a lot of people in the medical profession, use the term substance abuser...personally i told him to consider me an alcoholic because the term substance abuser gives me an image of someone sitting under a bridge sniffing glue...
When it all boils down to it thought you and i are drunks pure and simple, call it what you want as long as you accept this reality:-)