Does the symptom alcoholism mean that I have esophageal varices?

No. Esophageal varices are swollen blood vessels in the esophagus that are sometimes caused by chronic alcoholic drinking. Not all alcoholics have it, and not everyone who has it is an alcoholic. It is caused by increased pressure in the vessels from a sick liver and elevated blood pressure.
Not necessarily. Alcoholism can be simply having a problem with drinking. If resolved early, there may not be any organic damage. Ev (distended esophageal veins that can burst) is most often a secondary problem from liver cirrhosis. Hopefully, you can stop drinking before this happens. Take care of yourself!