Why do STDs/STIs cause back pain?

I have been suffering from lower back pain for atleast 6 months, which wasn't really benefiting from physical therapy. 2 weeks ago I found out I had chlamydia (and I assume I've had it for about a year) and got treated. Shortly after I noticed my back pain seems to have gone away.

My question is this- what exactly causes the back pain that is associated with an STD like chlamydia? I can't seem to find any information beyond what you learn in an 8th grade health class. Is it from muscle inflammation or from your sexual organs being infected or... ?

Any info is greatly appreciated.