Welcome Chris,
I had two DUI's over a 30 year drinking period. The DUI's didn't make me alcoholic nor did they make me want to stop drinking. I wish I was smart enough to figure out after the first DUI that I was an alcoholic. I didn't know what an alcoholic is and what defines them as one. So I will give you why I label myself as an alcoholic. I am an alcoholic for two reasons, 1) I crave more alcohol when I drink it. 2) I obsess about drinking alcohol when I am not drinking it.
Non-alcoholics don't crave to drink more when drinking.
All the shame, guilt and remorse that you are feeling will go away with sobriety. The first 30, 60, 90 days are the toughest of all. It does get easier and it is much easier if you get a sobriety program. So I would suggest using AA, SMART, or some other popular recovery program.
Good luck