both my girls were born at 36 weeks due to premature rupture of membranes (waters breaking too early)
I had to go in and get things checked but with dd1 they sent me home with oral antibiotics and told to come in 48hrs later for an induction (my cx started about 10hrs after waters breaking and she was born the same day). I was told that it was unusual with a premature labour to be sent home but was very grateful for the ob who suggested it as labouring at home was much more pleasant
With dd2 my waters broke and cx started immediately so when I went in for a check (as it was premature labour again) I stayed in hospital and delivered dd2 5hrs later

I would always call the hospital when my waters broke