40 Weeks & Have Not Delivered

I’m growing anxious that I’m standing at 40 weeks today but have yet to delivered. No obvious signs of labour. Perhaps just the normal slight cramps similar to what I encountered in pregnancy. This is my first pregnancy At 39 weeks + 4 days, Dr did membrane sweep and told me I’m 2cm dilated. Came back home i don’t know if it was discharged or partial mucus plug with tinge of blood. I don’t know if that’s mucus plug or the cause of the membrane sweep. I am growing anxious. I will have to self admit at 40 weeks + 3 days and be induced if i do not deliver by then. I do not want to be induced as i heard it’s more painful. Is that true?