40+2 turned away at hospital

I’m 40+2 and I went to the hospital at 5 am yesterday because I was having sharp pains which I thought were contractions because they were unbearable and i also had diarrhea with them .. I got to the hospital and the dr said I’m 3 cm dilated but sent me home because they don’t want to induce me bcs it’s increases a chance of c section. I’m now talking to a friend and she said they wouldn’t let her go past her due date so they induced her and she gave birth naturally.. has anybody else been turned away 3 cm? Or did they keep you and induce you?