Welcome to SR RolyPoly.
Going to AA is a good start. Keep in mind they won't solve it for you but with you. You need a plan to handle everyday situations and the support AA provides will support that plan.
No child wants to think a parent is an alcoholic so if you are only using your son to gauge things of course he will say you are not.
For me being an addict or alcoholic is about when the drinking or drug becomes the dominate thing in my life. I can assure you it did.
Post a lot here. Join in on any number of regular conversations. Post before you drink. And open your heart to the idea that you really can stay sober.
Ken