I should have replied you a couple of days ago ,but cuz of the bad internet connection, I am late. You see ,i am a graduate majoring orthopedic .Your problem is certainly orthopedical,but cuz of deficiency in clinical experiences and limited knowledge, I cant figure out your problem . Though I kind of sure that if the problem bother you all the time, it is severe.
Your symptoms characterized as night pain,or rest pain, colicky pain, moring stiffness, I think there may be possibilities of infection,tumor,spondyloarthropathy, or viscerogenic back pain. Cuz you mentioned you cough ,i am wondering if you are going through fever,weight loss,malaise, if it is true , I think the possibilities is higher.