They rarely give any context in the show as to the passage of time. I originally commented to my wife that Arya seemed to heal very quickly, but then I filled in the blanks and concluded maybe she had been sleeping there for a month. Lady Crane was shown reaching up to a top shelf to get more Milk of the Poppy. Maybe she had used all the stores she had in the medicine cabinet nursing her for a few weeks, and had to reach up to her backup supply. It's a fantasy drama not a reality show.
To soundcrib's point, I think the waif wanted her to suffer, despite instructions to give her a quick death. For not following instructions, in the end she paid the price in Arya's place.
Is it lazy writing for dramatic effect? of course! But I fill in the blanks myself. I notice it seems the fan service and lazy writing has increased since the show passed the source material.