Welcome Stw33,
Depression and alcoholism, in early sobriety, have pretty much the same symptoms. Depression is a recognized illness, while alcoholism, if it is left untreated, often manifests in feelings of self pity and uselessness.
The medication you have taken is a treatment for depression. There is no medication that treats alcoholism. That tends to be a matter of choosing and following some kind of recovery plan, and usually involves a certain amount of work.
Alcoholics that are misdiagnosed with depression can often end up with undesirable consequences from the medications, so it pays to be absolutely honest with your doctor and understand which of the two problems you are trying to treat.