That white stuff sounds like some of your mucus plug, when I lost my mucus plug I was 3cm at 39 weeks but went into labor 2 days later I stayed 3cm for a while then I was 6cm the next time they checked me before u now it it was time to push. Congrats and Good luck, it's a precious memory.
With my second son I dialated to 5 and then labour stopped and I had him a month later. Some tips to start cotrations is lots of sex cause sperm will help you go into labour and nipple stimulation works well too. Good luck