Due date?

I have a question, when I went in for my first appt my dr gave me a due date of 8/9 but when I went in for my next ultrasound I was 4 days behind, went back again a week later and still 4 days behind. My dr didn't want to change my due date to 8/13 because it wasn't 6 or more days. But the other dr said she would go with a due date of 8/13. When I go to my dr it says due date 8/9 on my chart. Should I just go based off of that info? I just feel the ultrasound showed growth consecutively at 4 days behind so it was pretty accurate. Help?