Could the due date that my scan gave me be wrong if I know exactly when I conceived?

It's very unlikely, as a dating scan at 10-13 weeks is probably the most accurate way of dating a pregnancy. But you should remember that even then, there is up to a week's leeway either side. Also, don't forget to add 2 weeks on to your assumed conception date to give your calculated gestation (number of weeks)-which is always taken as if it was from the first day of your last period.