I don't know if this is the real deal or not, help

I've been experiencing contractions since I woke up at 6am. At first I assumed they were braxton hicks but they kept coming consistently. Also I have been experiencing pain in my lower back with each contraction. After about an hour I decided to start timing them. Between 7 and 8 my contractions averaged at about 5 and a half minutes apart each at about a minute in the beginning to over two minutes after an hour. I decided to wait a few hours before I start timing them again. I drank a few glasses of water, in case I was dehydrated. I assumed they would have gone away by now if it were just braxton hicks but it hasn't let up since. Also starting to feel the urge to poop as well with each contraction now. I'm a FTM and not sure if this is the real deal or not. I don't want to go all the way to the hospital simply to be turned around. Currently 39 weeks and 3 days. My water hasn't broke and I don't recall losing my mucus plug yet. Also at my appt Monday my cervix was still closed. Not sure what to do. Help.