its really not advisable to pop sleeping pills at this moment becoz its really bad for your baby.
I had induced labour but was at full term.
In this case i think its good to have a discussion with your gynae. The whole duration of my induced labour lasted 16 hours. They start by inserting a pill at the cervix area to soften it so that it can start to dilate. This pill will be inserted max 2 times i think, at 4 hours interval. After that my cervix only dilated 2 cm after the 2nd pill was inserted. I was also on antibotics drip becoz of waterbag burst, so to minimise infection they put me on oxytoxin drip to speed up the process of dilation. Within 8 hours my boy was delivered via natural with forceps.
SO i guess its helpful to discuss your option with the gynae and see which is best to address your concern now. He can also advise on the possible complications from the induced labour.