First pregnancy!

So I found out a week ago I am pregnant. I had recently started taking birth control again but little did I know my little miracle was already in there. I go to the Dr Wednesday but I have heard the Dr bases your due date off of the first day of your last period. If this is true I am 6 weeks and 3 days. I have been having light spotting and cramps throughout the day. I also feel full very fast. Is this normal?