Does it matter whether I go to AA or NA?
Well this is just my opinion and not my experience so take it for what it is worth, if alcohol leads you to opiates then why not start out with AA or of course do both. There are no rules in AA, nor AA I believe, so going to both should be honkie dorie.
The only requirement for membership in AA is the desire to stop drinking so there will be no problem there at all.
I know quite a few folks in AA that are like you and easily identify them selfs as alcoholics.
I have heard it said in the rooms many times that it is not how much one drinks, how long one has drank, nor how often they drink that determines if one is an alcoholic or not, what determines that is what happens to one when they drink.
Using that as a definition, if drinking leads you to opiates you qualify.