I relate very much to your story. The painful childhood, death from cancer (and my own 2 cancer scares), loss of a relationships, etc etc.
Sooooo. Hmmm. First of all, you aren't in recovery. Yes, you're drinking less, but you are walking a very very fine line if you are alcoholic. And you're lying. I'm sorry if that hurts but lets keep it real. You are seeing a psych, taking meds and dealing with substance use disorder which is a mental illness. And you're considering marrying a woman who has no idea. Yikes. Our secrets make us sick. Lying is never ok, no matter what the lie is. Alcoholics, me included, are expert liars and manipulators. There is no logical rational here.
Marriage is for life and it is a HUGE commitment. She has the right to know. That or risk hurting her in an irreparable way and eventual divorce. So yeah, you owe her the full truth. You owe yourself that.
If you are alcoholic then you need to get into action and grab recovery with both hands.
Good luck.