I need help!

I am 39 weeks. I went to my doctor visit yesterday and baby girl still has not made any attempts to move down or want to come out. She is still so high that I could feel her kicking my boobs (At least that's what it feels like). My cervix hasn't even bothered to dilate, not even half a centimeter. So he wants me to come in on Monday for an ultrasound and to monitor the baby and check the fluid around her. I asked him what if nothing happens by my due date, which is next Friday the 22nd. He told me he does not want to go pass my due date. So I told all this to my mom. Well she starts asking everyone and freaking out. Getting everyone's opinions. She said that he needs to wait up to at least 10 days past. He told me the reason he won't go past my due date is because I can become high risk and that sometimes it's not good to leave the baby in there any long. Have any of you ladies experience this? What should I do? Should I voice my mom's concerns to the? Thank you everyone for your help!