In my opinion you should do what the doctor says.
Who cares what people at AA think. Taking anti depressants is not the same as abusing alcohol.
I had my anti depressant dose doubled when I quit and it's definitely made it a lot less painful. I don't consider myself to "have a problem" because of them any more than I consider taking aspirin for a headache to be a problem.
You can't get a buzz off anti-depressants either, so the potential for abuse is non existent.