Well, only you can say if you're an alcoholic.
It's not how much we intake it's how it affects you.
I've failed many, many times. Quiting required action, like staying out of bars and other triggers for me.
You feel bad now. Remember that feeling. Think the first drink through to the end and where it'll lead. This helps keep me sober.
You're definetly not alone. Best to you and pick yourself up and start again.