First of all, congrats!!
It is not unusual for "due dates" to change as the pregnancy progresses, because of ultrasounds. I had an ultrasound at 7 weeks because I thought I miscarried. They told me a due date, and then they said that when I came back for the 20 week ultrasound, the due date would likely change.
By choice, I did not have any more ultrasounds. I knew my baby would come when he was ready, and I felt like he didn't need constant monitoring. He arrived 38 weeks after the start of my last period.
Like someone else pointed out, 37 weeks *is* term. A normal pregnancy can range from 37 weeks to 42 weeks.
My friend was in the same boat as you, as far as having a planned c-section. She went into labor the day before it was scheduled, and they just did an "emergency" c-section on her.