Daphne, you are going to get some tough talk here: hope it doesn't drive you away. I think it is impossible for anyone here to tell you if you are an alcoholic or a heavy drinker. It is a completely personal self-acknowledgement: only you can make it.
There is a difference between a heavy drinker and an alcoholic. A heavy drinker can cut back and even stop by making some changes in their lifestyle. An alcoholic usually does not ever succeed with moderation: an alcoholic will have a powerful mental obsession to drink and physical cravings.
You have made a very good decision to see about your liver problems. I would, again, suggest you talk with your doctor very honestly about your drinking. You may have your doctor tell you again to stop.
If that is the case, you have a lot of support here: we have all taken that journey to quit and stay quit, so, I hope you keep coming back. Good luck with the doc visit!