Does it matter that much?
For me, I'd say you definitely seem to be a problem drinker, if you go straight back to a binge after a hangover that horrific.
If I were you, I'd try giving up and see how much better you feel after a couple of weeks, you are unlikely to feel great the first few days.
As for the cognition, you'd have to see your doc, but some reports seem to be saying that regular binge drinking can have a significant effect on memory, brain function etc.