Thing is, it can be caused solely by too much relaxin (hormone), though this is uncommon - usually it's partly that and partly the pelvis slipping out of alignment. In the latter case physio manipulation and exercises can help a lot, as can some osteopaths. But if it's the former, then all you can do is cope.
My first pregnancy - my great osteo and an expert NHS physio both confirmed my pelvis was perfectly aligned which meant there was sod all they could do apart from talk to my work, ban me from commuting, suggest some exercises, offer a support belt, tell me where I could get a wheelchair, and reassure me it should get better soon after birth, especially if I came to their postnatal exercise classes. Which it did, luckily, as three months of using a wheelchair was a right pain.
Currently in 2nd pregnancy, 29 weeks, had really bad SPD pain at 8 weeks (only began at 16 weeks last time), was very worried, but this time the same NHS physio team have manipulated me and put me on a strict exercise regime, and I can walk 2 miles a day - slowly and carefully, but that's a huge difference to being reliant on a wheelchair to go 100 yards!
It probably helps that this time I know all the stuff in the leaflets - pace myself, keep my knees together at all times especially in bed and when walking, take lifts/buses whenever I can, clench my buttocks and lower abdominal muscles when getting up/down or walking, etc.
I hope you have an NHS obstetric physio team as good as mine, but if they say it can't be fixed they aren't necessarily wrong!
Also you can be prescribed codiene with your paracetamol which I'm allowed 60mg 4x daily, and used that much last time, but this time I only use it to help me sleep - getting a decent 6 hours sleep makes everything more bearable.
Good luck!