Congrats on 11 days. Drinking any amount of alcohol would be detrimental to your liver's recovery at this point so keep up the good work on your sobriety even if your doc didn't say anything about it. And definitely don't use that as an excuse to start drinking again (the fact that she said nothign about it )
A fatty liver can have many causes though, so your diet and exercise ( or lack of ) could certainly be involved.
If you have concerns it's never a bad idea to get a second opinion, but please stay away from Dr. Google.