It certainly does sound like sciatica. I had surgery for it in 2000, very minor, removing material from a ruptured disc that was pressing on the nerve. As I now have scar tissue, at least two ruptured discs, and spinal arthritis I get flare ups from time to time. I have had good results with a brief run of steroids to reduce the inflammation, but the original surgery was very successful as I am free of symptoms most of the time. My neuropathy has advanced enough to mimic many of the symptoms but there is still something different about the sciatica attacks as I feel an ache in the lower back and the pain wraps around under my foot on the left side. It does all run together and get confusing.
Your neurologist should be able to tell from an MRI if you need to see a neurosurgeon. You sound like you are suffering quite a bit. I was on bed rest for several months before they decided on the surgery, I could hardly walk. I hope that you get some better answers soon. I really do not see how a rheumatologist would be able to diagnose you from such a cursory exam.