They start counting based on the first day of your period, so it sounds right to me.
U/S is a guesstimate. LMP is a guesstimate. The drs are trying and are helpful but the best they can do is a guesstimate. You know you best. Congrats :)
The ultrasound dates are approximate based on size of the fetus. You could have maybe ovulated a few days earlier than you thought, or implantation may have occurred a day or two faster than average, or baby could just be growing like a weed in there. There is a possibility that when you go in for you 20 week ultrasound that the dates may line up a little more as you had thought. There are so many variables that a week or 2 is not a big difference. With my last pregnancy I got a bfp almost 9 days before my missed period!! Congratulations!!
U/s can be off up to 2 weeks, you might just have a big baby. They all grow at different rates. Congrats on your lil bean!