I'd encourage you to read more on the physical issues/possible treatments of alcoholism. Joseph D. Beasley, MD has several books. Joan Mathews Larson has a website and the book "Seven Weeks to Sobriety" goes into great detail about the biochemical issues and recommended daily supplements/dietary changes.
The sugar (ice cream) cravings could be due to hypoglycemia. Some studies show about 90% of us suffer from it when quitting. Dealing with it by gorging on sweets will make sobriety much tougher - the sugar cravings can seem like alcohol cravings. Your body NEEDS the carb fix, and got used to alcohol as the preferred vehicle. Depression, anxiety, fatigue, insomnia - all common for hypoglycemia and alcohol withdrawal.
What worked for me, and I drank all day every day, was totally cleaning up my diet, taking a handful of supplements every day, and exercise. No sugar or simple carbs like white flour, little caffeine, lots of protein and vegetables some fruit. B-50 supplements, Niacin, EPO, fish oil, vitamin C, vitamin D, calcium/mag, and others in the beginning.
The sometimes crushing depression went away and hasn't returned. Haven't felt better for a decade or more and it's been 2+ years. Lost 40 pounds, and am a new person, physically and mentally. With AA, life couldn't be better.
Do the reading. If you don't buy it, that's fine, but it DOES work for some of us and when it works it's a miracle.