Won't Dilate?

 I've heard mixed stories about dilation being genetic but my mom was allowed to go 2 weeks over with me. I ended up being 9lbs 8oz. At 42 weeks, her water broke at 530pm as a slow trickle. Dr told her to wait it out until her morning appt. Her water finally gushed at 10am after that appt and she was dilated to a 4. She went to the hospital and at 9pm that night never dilated anymore or had strong contractions and had to have a c section. She didn't progress. They allowed her to go 2 weeks over with a 9 1/2 lb baby she couldn't birth. I'm an only child (and this is mostly why) so I have no other births to go off as far as reference. I'm terrified the same will happen to me. 

I have an OB appt tomorrow and I'm going to talk about it then. I couldn't even have a membrane sweep because I'm too thick. I was told at 37+6 my baby is already 8lbs.