I have the same thing happening along with sharp pains in my lower stomach. I'm 36 weeks today. I trying a heating pad for my back and it helps a bit so maybe you could try that it may help.
Drink lots of water and lay on your left side and see if it gets better or worse. They will want to stop labor at this point so go in if you feel like you are in labor.
Bless. Im same as you but 31 weeks 4 days. My back has been hurting aswel my midwife sd focus on your contractions if u hv any and time them if they get very pain full with period like pain then ring hospital and go in to get checked you may be in preterm labour. Sry dont want to scare you. Tk care. X