You might be right, it might be that the pharmacy won't accept the prescription until the last one has run out, rather than when the doctor will prescribe a new one. Regardless, it's a really common complaint in ADHD support groups I'm a member of with members based in the US - every month is a hectic hoop-jumping exercise that, if you didn't know better, almost seems designed to be difficult for people with ADHD.
I think it's more like a week before.