Why do they depend on ultra sounds?

I went to the hospital today since I thought my water broke last night. I got pregnant May 16 2010. The doctors say my due date is March 13 2011. My last period was April 28 2010. I got on a pregnancy calculator and according to my last period my due dat was supposed to be Febuary 2 2011. They told me they don't go by last periods they go by how big the baby is. What if my child is just like a runt or he is smaller than usual babies? How big is an "average" baby? So do I have to chance that I really am only 35 weeks and then have him go overdue and die because the doctors are idiots? Im just really frusterated. Why do doctors make you feel like your the worst person in the world for not getting prenatal care because I didn't have the money or because when I signed up for Medicaid they ****** around with me my whole pregnancy and no doctor would see me? Am I wrong? Please don't be rude I just don't understand why Im getting ****** around. And since when did you have to schedule to be induced. I know Im 41 weeks and 1 day. I have counted every single day since I found out. My periods are were like clockwork thats how I found out so fast. I wasn't even a month pregnant when I found out.