I don't want to scare you, just share my experience with you.
My hubby moved some furnitures at home and then I lost my baby immediately last time. (2 year ago) So this time, we want to move but I have to wait 1 more month until my baby is born. I also went to see many apartments this month (37 weeks), no problem, when you enter the flat, just say, 'excuse me, I just come to see the flat only.' I rent the new flat already and my hubby will arrange everything when I will be in the hospital. I can go to the new flat with bb once check out from the hospital.