I generally don't feel the need to point out unrealistic/illogical scenes in fictional tv shows but the Dr. in the pharmacy and with the car was just plain dumb.
They're doing all kinda dumb stuff. I think with the doc she was trying to build up courage or something. Extremely ill-advised, but somewhat understandable.
Eugene is extremely lucky they ran into Daryl's group, otherwise he'd have been the only leverage they had to get into Alexandria, and that likely wouldn't have boded well for him. And I'm surprised Daryl didn't notice a dozen guys creeping up on him. City life is making him dull.