Technically this is a dicey question. There are psychological tests that are purported to measure alcoholism, but all such tests are subject to error. There is no physical test that I know of that renders a definitive answer to your question. If there were such a test, I think it would be in wide use.
The term "alcoholic" is probably up for debate. God knows, drinkers test themselves enough of the time, some always getting the same result, yet fail to admit they might be alcoholic, anyway.
I remember a clever statement that resonated with me, however: "If you are struggling to control your drinking, you don't have control over your drinking."
This should be enough to tell a person that he has a problem, and I don't know what more he should need.