Due date and venting

40 weeks today had a membrane sweep. My Dr says if it works it will within 48 to 72 hours. Those of you that had it done and worked when did you start having symptoms of labor?

I'm feeling upset so I'm just venting but we scheduled an induction. L&D had 7/30 available. I feel like that's too far away than I expected. My Dr says more than likely we will get moved up sooner because someone will have their baby before then. Does anyone have any similar experiences?