I don't endorse lying, but I would say nothing about my struggles with alcohol to anyone at work.
Coworker: "Oh, Allie! How do you feel? What happened?!"
Allie: "I haven't been feeling well, and I took some time to take care of it."
Coworker: "Well, okay, but...What happened?!"
Allie: "It's not personal, but I don't discuss such matters at work."