38 weeks-no sign of labor

Got a little smile from my girl today it looks like she’s having fun in there. My cervix is still not dilated and there are absolutely no signs of labor. Due date is 1st of February and I’m hoping that she will come a bit earlier even though that my only suffer is heartburn but the doctor started to prepare me today that I might be overdue and in this case I have to go to the a hospital at 8th of February for induction.. First baby so I’m super curious what will happen in the next few days/weeks🙈