Dentists

Here's my history:
I'm 35 - I started drinking at age 14, my parents rarely drank & never really had alcohol in our house (I do have family members who are alcoholics- Aunts/Uncles/Grandpa).
I started binge drinking in College/early 20's being disrespectful to women occasionally & got a DUI at 22 & blacking out in my mid to late 20's.
By 30 I reduced my drinking significantly & got married/started a family.
Here's my problem: I have only ever drank on the weekend & not every weekend (Friday/Saturday - rarely does it spill over to Sunday's where I'm hungover for work).
Also I never crave alcohol matter of fact I cringe thinking about drinking especially when I'm hungover- I just drink cause I'm bored I guess or stressed.
I rarely drink - typically ONLY 3-4 days per month & I'm fine I can quit/stop after a few but out of those days I'll have just 1 day per month where I binge drink & predictably blackout/do something stupid & I'm hungover feeling guilty. People all say "that's how I started weekend drinker then it was every day" well for me from day 1 to now its been consistent.

I was sober for 9 full months when my wife was pregnant & it was easy here is how/why I managed to stay sober for 9 months:
I went out to celebrate one night -drank & walked home (bar was close to my house) tripped on a sewer & bashed my face into the side walk & came home to pregnant wife with my face covered in blood. I said to myself I've got a child on the way & can't be doing this.

I know drinking has caused me problems but I never crave it & I rarely touch alcohol so it's hard for me to keep a day to day pattern for keeping sober.
Is anyone else like this? What can I do?
As I've gotten older hangovers have gotten horrendous & now with children even a mild hangover is a nightmare!

Am I an alcoholic?
How do I stay sober when I rarely drink?