There are other critera to EDS than just joint hypermobility. You dont say which type your sister has but some of the types can actually be tested for through skin biopsy or urine testing. Also, just for the record, there is no such thing as 'meds for EDS'. It is a totally hit and miss approach that usually takes people years to figure out and what works for one, most likely wont work the same for another. I do suggest though, that you get refered to a pain clinic as they should be able to help you manage the pain and might be able to give you some answers.