Sounds like your body is getting ready! I wouldn't obsess over whether it's "false" labor or the "real" thing. You'll know when it's the real thing, believe me, and meanwhile, every symptom means you're getting closer. Is this your first? Remember that you're not overdue until 42 weeks--your baby is cooking to perfection, so don't agree to any attempt to force him/her out before s/he's ready, barring any actual medical reason.
Hang in there! The waiting is hard, but try to rest as much as you can and enjoy these last days!
It is hard to wait!
Like the PP said, past due is when you are past 42 weeks (says someone who has delivered two children past due... 42 weeks and 43 weeks). I would be patient and just let the baby come when it is ready, barring any medical reason why it should be encouraged to come out sooner.
Sounds like your body is getting ready. False and real labor are on a continuum and lots of progress can be made during "false" labor. Make sure you are very will hydrated, nourished and rested. Keep active since movement is always helpful in labor.
If you are getting close to your induction some things that can encourage more contractions are sex (if your DP can muster up the strength), orgasm with or without sex, nipple stimulation (even with a breast pump). Maybe you could talk to your midwife about doing a castor oil induction before you go in for your medical induction. She can also strip your membranes again.
Good luck, I know it is hard to wait but you will be glad you did l- your baby will be too!
Ooooh.. induction is SO risky! Induction in first-time moms can lead to c-section rates as high as 50%!!!!!!!!! Now I'm not going to lie, there is some evidence that the risk of stillbirth goes up at 41W, but yet the actual average gestation for 1st time moms is 41W1D!! Yup, 8 days "late" is the actual average! Google "Mittendorf length of uncomplicated human gestation" if you want to see the results. The book "Gentle Birth, Gentle Mothering" by Dr. Sarah Buckley had a lot of good info too. Just being past 41W is not a good medical reason to induce, IMO.
My hospital-based MWs wanted me to do twice-weekly NST and AFI starting at 41W, but didn't push to induce until 42W. Even at 42W, they were totally cool with me waiting. I went to 41W4D and asked to have my membranes swept (for the first time.) We never even made the appointment for induction.
I started having the same sort of constant crampiness you describe right after the membrane sweep. No rhythm, no 'coming & going' ctrx - just constant dull ache. But I did have rhythmic ctrx start 2 hours after the sweep. As PP said, you will know when it's the real thing, don't worry. Even one of my MWs said that to me too.
I know the wait is hard, miserable actually, but please PLEASE let baby pick his own birthdate - it will make birth SOOOOO much easier on you & easier & better for baby too vs induction. "Due dates" are "guess dates" - there's nothing wrong with birthing a couple weeks before that date (at 38W gestation) why should we be so worried about birthing 2 weeks the other way?
Besides, unless you were charting your cycles or had a very early ultrasound, you could actually be not as far along as you think! Due dates are based on your last menstrual period, which assumes you ovulate & conceive on day 14 of your cycle - but of course that is just stupid. We're humans, not machines, and women ovulate on different days, even the same woman ovulates on different days different months. I normally ovulate day 13 or 14, but this baby was conceived day 22!!! The stress of my dog nearly dying & needing 5 days of hospitalization delayed my ovulation.