Past 38 weeks....

Anyone delivered past 38 weeks with twins?? I'm 37.1 weeks and had a doctors appointment today. My doctor made it seem like I could go all the way to 40 weeks!!! I've heard so many stories about not letting them go to far over 38 because risk of still birth. They're both good sizes at 6p7oz for baby B and 6p4oz for baby A. Both head down and have been since June. Heartbeats good. I haven't had any complications except low iron halfway through but it's good now. I'm just a FTM and am terrified of something happening.