Alcohol withdrawal does often start mild in the beginning and peaks at its worst after several days go by. So it's not unusual, but still a wise decision that you're seeing a doctor, as there's a possibility those symptoms could be alcohol-related but not withdrawal-related.
I've never talked to my family doctor/general practicioner about drinking, as I haven't had one in a very long time. I have talked to doctors in hospital before about my drinking. I did get a short, "here's the facts" lecture about what alcohol was doing to me and what I might expect if I didn't quit. It was hard to hear, even though I needed to hear it, but it was professionally done and didn't strike me as moralistic judgment. I would've expected the same tone if I was being seen for high cholesterol and admitted I ate Big Macs six nights a week.