Sounds like you have the exact type of allodynia I have. Same symptoms, and location on the body. I got mine very suddenly in late March of this year. I've been diabetic for 40+ years, and on insulin for most of that time. I don't have trouble sitting in a chair, as long as there's no movement across my back. My husband and I recently took a road trip, and riding in the car, with the seat's movement as we drove across the pavement, and especially hitting potholes, was, I would say "agonizing" but it was a month long trip so I just had to buck up and tolerate it as best I could.
The weird thing was that no doctor I saw, dermatologist, endocrinologist, PCP, knew anything about it. Had never heard of it or knew what it was called. It wasn't until I saw a neurologist that I got any clues (or hope) about what it was. He said that it was probably related to my diabetes AND my alcohol use. That the nerves would regenerate in about 8 months if I kept my diabetes under control (I always have done) and quit drinking. I didn't think I was drinking that much, but. . .so I quit one month ago, and we'll see.
Shortly after the allodynia started, I also started having twitching and jerking in my hands and legs, and trouble with my balance. The neurologist said that would get better, too. And it has! After one month w/o alcohol. So I have hope that the allodynia will also get better.
So, forgive me if all of this is way off track of what you are experiencing. I don't know if you drink at all, or have the ol' diabetes. I don't have fibromyalgia, so our paths may diverge a lot. I do hope you are seeing the proper doctor, and get good treatment. I forgot to mention that I take Gabapentin (Neurontin) for the pain, and it helps a lot, though doesn't completely eliminate it.
Good luck to you, and best wishes.