I’m one of the people for whom it took 2 years (more, actually) to feel mostly normal again after quitting drinking. My drinking patterns followed a perfect-storm recipe for the development of kindling and PAWS, plus I believe individual susceptibility varies, and I was way out on the high end of the curve.
I wish I could find the reference I read which said that occasional binge drinking can actually be harder on your brain than daily drinking. It was from a reputable source such as NIAAA (National Institute on Alcohol Abuse and Alcoholism). The gist of it was that it's actually the withdrawal process that causes the brain damage, and repeated bouts of binge drinking put your brain through a whipsaw of habituation/detox cycles that throw it way more out of whack than drinking the same amount more evenly would.
The answer to your question seems obvious to me: If you are concerned at all about the symptoms you're experiencing and want to prove beyond a doubt whether alcohol caused them, simply stay abstinent for long enough (considering your history, 6 months is probably a good trial period) to see if they start to go away. If they do, then you have your answer. If they don't, another visit to the doctor will be in order.
If you really don't have an alcohol problem, the idea of going without it for 6 months shouldn't trouble you at all.