a few questions

i'm a first time mom and have been struggling, i don't have a regular OB i go to the department of health because my insurance is all over the place. i started going weekly but i'm 37 weeks and 4 days and i'm wondering if the dr was supposed to check his weight, and my cervix? like if that's a normal 37 week checkup, because mine wasn't checked. they checked his heartbeat and he told me the baby was head down but that's all. i'm just wondering if i should go to the hospital and have them take a look to make sure everything is going good.