I'm also 37 weeks and cervix is still closed but if there's no progress by week 39 I'm going to get induced my doctor doesn't want a bigger baby or any complications I was induced with my previous daughter and she was fine. You should ask your doctor about inducing you.
You cant cus your baby isnt ready yet. Your baby will much healthier staying in ur tummy.
I've another 3 weeks I'm afraid plus if u go over due ... Baby will come when ready