Your baby is ready between 37 amd 42 weeks :) the due date doesn't really matter so much.
A Sono done by a doctor late in pregnancy, after 25 weeks or o, can be off plus or minus 2 weeks due to the fact that not all babies grow at exactly the same rate and measuring long bones for dating that late may be off. I'd go by what your primary doctor says because he obviously has early dating on you.
A due date is just a time line. I would stick to what your so c tor says. Your baby will come when it's ready. If they are already stopping it with shots chance are higher you may go early. Good luck. I know it's confusing. I was told the same thing. It's mostly based on what your baby is measuring. Mine was always a week behind.