I don't know which came first - the depression or the drinking. I've been on sertraline for depression for a long time and will likely always be on it as it works to stabilize my mood. It's not a 'high' or anything like that, but it evens out the chemicals in my brain and makes me feel better about myself.
Sometimes depression is due to drinking, and getting sober takes care of that. But other times the depression is just made worse by the drinking and needs to be treated, so the depression won't persist after getting sober.