Do you think I have an alcohol problem that requires rehab?

I drink about two and a half gles of wine a night, by myself. I can't stop. I've been to AA twice & it didn't help, because it wasn't regimented enough. I occasionally drink three to four gles of alcohol and drive, but that is in a span of about three to four hours. I used to black out, but I haven't for over a year. I suck at work, making a lot of mistakes, but I know that is the nature of the job I do, NOT because I drink alcohol, unless I've killed brain cells because of it. I have drank like this for many, many years. I have an opportunity to do three months of outpatient rehab, free, per my doctor's recommendations and I would probably get State Disability in CA with short term disability at work, getting my full pay. I know this for a fact. Don't confuse this with Social Security. The problem is that I bet my previous work performance will be looked at more closely while I'm gone, making me be more in jeopardy of losing my job than I am now. I hate my job, by the way. Do you think I have an alcohol problem that warrants going into outpatient rehab & would you go forward with it, given my cirstances? Thanks.