Wondering if can induce labour

Currently 39 weeks 2 days. My last check up was a week ago and the doctor was saying I’m alr 2cm dilated and even did a membrane sweep for me. She said I probably will go into labour these few days but til now my water bag has yet to burst. My mucus plug has alr come out 1-2 days after my membrane sweep too. My next check up will be in 3 days. Not sure if I can ask the doctor whether it is possible to induce labour? Isit possible? I’m a subsidised patient with NUH, don’t have a gynae I am with. Is induction of labour rly more pain compared to waiting for waterbag to burst? And normally 2cm dilated by now….. shouldn’t there be some sort of progression…. More dilation. especially with the membrane sweep done #firsttimemom