I'm not a Dr, however, I have been through my share of back problems (21 total back surgeries in the last few years, and my 22 coming up in about a month)..
My advice would be to start with your primary care doctor first. Back spasms, etc can be very painful and can take some time before they clear up. On the other hand, you could have a disk out, or bone spur, etc. You would need a set of xrays and an MRI to get a good diagnosis.
Pain Management is very strict as probably most people here in PM can tell you. It is reserved for people that usually need long term therapy and usually with opiates (narcotics). That scares many doctors, so they will want a definate diagnosis before PM will take you on as a patient. And is also depends on your age. Not asking you to disclose your age, but by your post I gather that you're younger amd PM docs seem to stay away from young patients. Not that I'm saying its right, pain is pain, but that seems to be the norm in todays age..
But if it were me (and it has been years ago), see your Primary Care and get some test done. MRI's are spendy so hopefully you have good insurance...
Best of luck to you!