Membrane sweep & induction

So im 40weeks and 1 day today. Im still dilated 1cm (for 3 weeks now, no progress) and my cervix is still really thick. My doctor stripped my membranes today and told me that it probably wouldn't work since my cervix is still thick. She told me I would bleed and have cramping. I haven't had any bleeding at all and no cramping either. Im getting induced Saturday but I really wanted to experience going into labor on my own. Has anyone else gone through this and still went into labor on their own? Also for you ladies that have been induced with a thick cervix, did you end up getting a c section?? Please feel free to share your stories! :)