Living sober I experience a happiness way beyond what I felt when using. I am an agnostic and attend AA without any problems doing so. For me the religious parts I avoid are the prayers, and I simply don't pray.
You've laid out a progression of drinking that may lead to severe illness.
I would concern myself with stopping drinking instead of reasons not to get help.
I hope that you do not need to experience the tragedies and devastation I had to make me decide to quit drinking.
Best to you and may recovery be speedy.