Hello there and welcome to Kickas
From the few symptoms you mention, the bloodwork and family history I think unfortunately it is safe to say you have AS.
Unsure why the doctor cannot figure that out... may be looking at a 1970´s medical book. Currently you may not have MRI proof.. but it will come with continued inflamation/pain if untreated. Not everyone has elevated inflamation markers in blood either.
If cannot get treated properly for now... can look at Omega 3/Fish oil.. some have success with that, Ibuprofen for some temporary relief of modifying diet to see if helps.
I would continue working with the doctors and educating them on AS so you can get a proper diagnosis.
Best to you,
Tim