Hi, thanks for your comment. To note - I'm one of the current authors that cover addiction on HealthyPlace, not the original author of this article.
First of all, hats off for taking corrective action. You've apologized for your actions and respected the other person's space to process everything. I've been in this exact situation on more than one occasion many times, and the feelings of shame and guilt can be overwhelming. It sounds like you're evaluating this with honesty and looking at taking steps to change, which is the main thing.
It's a good idea to try AA - it helps many people deal with heavy drinking and alcoholism, and most areas have at least one weekly meeting.