This question, "Am I...?" comes up regularly on this forum. I think the essence of the collective answer is,
"If you have to ask...., yes."
That means: You have a dysfunctional relationship with alcohol; you've tried to quit drinking and failed, you cite other life problems that are related, once you start drinking you don't stop, etc. And by 'you' I mean just about everyone who asks this question, including myself.
So, whatever it means to be an alcoholic (and I personally think there are thousands of individual ways to be alcoholic or an addict, and myriad levels of functionality are consistent with these), yes.
Now what is the best plan for getting free of alcohol and getting your life back on the bright side?
For me it was: M.D. consult, referral to OP rehab, AA, SR, AVT, dogs and horses, divorce, reading, and running.