I had a similar thing. I have never had back problems but after DS my lower back was really painful especially when I lay down at night I would hate rolling over in bed.
I ended up going to physio as I have an old tailbone injury and it was also sore. I then got referred to a muscular skeletal doctor who has found out my right pelvis keeps dropping so it is making my back sore (and aggravating old tailbone injury).
He manipulated it back in (didnt hurt) and I havent had a sore back since. It does still drop occasionally so my tailbone gets sore so I have to go back and get him to pop it back again.
He said it is common after childbirth, especially if ventouse or forceps, which is what I had.
Hope you gfeel better soon