What would you do?

So, I've been having contractions 10 minutes apart since Thursday night and developed back pain at like 3-4 AM this morning. The contractions aren't horrifically painful, but the length of time has started to make them overwhelming.
I have an appointment tomorrow evening and I'm wondering about asking my OB about trying to speed things up. I don't mean an induction - that's something I want to avoid if possible - but maybe sweeping my membranes or something. It's not something my doctor does at all until you're overdue but I'm thinking about asking just because of how long this has been going on.
Would you? I'm 37 1/2 weeks and I feel a little guilty because I'm only just term. But these contractions and everything aren't stopping, so you'd think he'd probably be ready, right? I don't mind going to my EDD or even overdue like I did with my son, but I feel ready to die right now.

Maybe asking if they can stop the contractions instead. With my first the dr was able to give me a shot to stop the contractions that started to show signs of preterm labor. I had it once at 36 weeks & again at 38 weeks. Ds was born 5 days before dd.