If your waters have broken technically your labour has sort of started so you would be augmented not induced (induced is when nothing is happening sort of) augmented is sped along. It really depends on the hospital your birthing at but many places are happy to induce or augment with a prior C/S especially if things are favourable (meaning your ready to go which you probably are if your waters in deed have broken). Smaller places are often not happy to care for you labouring with a past C/S but most tertiary (larger) places are happy to care for you. It really depends on what your hospital policy is.

If your waters are broken often you will go into sponatenous labour within a day or so (not always but most of the time) but either way I would confirm if its your amniotic fluid as like mentioned early there is a risk of infection. Amniotic fluid often has an after sex smell or BO smell.