Sorry to hear that you are experiencing this new sort of pain. Sounds more like neuropathic than musculoskeletal pain to me based on your description, but a pain specialist would be the one to know for sure.
If the doctors you are currently seeing won’t take you seriously then it is time to find a new doctor. I know, easier said than done sometimes, but it is important that you avoid being harmed more than helped when you visit a doctor.
There are some recent scholarly articles available online that address the incidence of neuropathic pain in EDS that might be helpful in your quest for answers.