I don't know how many tests (ie: MRI, xray, etc.) you have had, but typically sciatic pain manifests itself by local pain in the buttocks, often radiating down the back of the leg. The lack of relief you are experiencing with position changes or analgesics does smack of nerve type pain, perhaps a disc herniation or muscle spasm impinging a nerve. I would make sure to get an MRI if insurance covers, and that can confirm this type of injury.
I had similar complaints earlier this year, and given that I had a history of back problems, I assumed I had sciatica inflammation again. When it got worse, I went to a neurosurgeon and he informed me the problem wasn't my back but rather my hip. I mention this because you said you had groin pain, and that is a very common pain complaint with degenerative arthritis in the hip. I ended up having my hip replaced in September, and I am good as new...back to full activity!
Whatever your problem ends up being, I wish you relief with your discomfort...I hope it is short-lived and easily remedied!