At the end of the day it is your decision. I have been going through the same as you and am up most nights with prelabour since 30 weeks and I am now 37 weeks (contractions get to 3 mins apart then stop!). It is exhausting and I have decided along with my ob to induce so he will be doing an internal at my app on friday.
Same thing happened with my last pregnancy and he checked me every app from 34 weeks and I was induced at 38 weeks by which time I was already 6cm dilated.

Goodluck with the rest of your pregnancy and relax.