They may do a sweep, I delivered 2 of my kids within 24hrs of having a sweep. I personally would avoid induction, my first was induced and we had a terrible time of it, lots of folk do fine, but if I were you I would hang off another few days, baby will be here really soon, the last few days are torture I know, I've been overdue 3 times and was 6 days over when I had my last baby on the 13th...hang in there, it wont be long :)
Just tell them you want to be induced before 42 weeks