FTM here too. I took warm baths walked bounced on the exercise ball pretty much everything and was only 1 cm. Don't let it discourage you though because I was due for a c section on the 28th because my baby was too big and they didn't want him to get stuck, I went from having zero contractions to 3-5 min apart just like that. And he decided to come Christmas day instead. So just because you don't think anything is happening it can also happen just like that! Oh and the bumpy roads brought them on and strong so try a really bumpy road. ;) GL being a mommy is the best thing in the world!! Although every little thing will make you worry.
Warm bathes really helped me (I lost my plug one night after a bath, and went into labor after another bath), also the membrane sweep from my doctor at 39 weeks!
I'm due on the 31st also. My last appointment I was a fingertip dilated and 70% effaced. My family is driving me nuts trying to rush this baby out. I have been walking and drinking raspberry leaf tea. Had sex a few times soon. I think I may be having a some mild contractions, but nothing definite. I don't want to be induced either. My doctor said they won't let me go more than a week past my due date. Good luck to you. I hope both our little ones decide to make an appearance soon!
I don't know if you had your baby already but I was 1 cm dilated on a Monday I went for a hike that weekend, went to my doctors appointment the next Monday and was 3 cm. that same week on Wednesday I had my baby after taking the castor oil the night before because I also didn't want to be induced. I had a very smooth labor and no runs :)
You should ask your doc about evening primrose oil! It worked like a charm helping me soften and dilate.