Can an STD cause lower back pain?
An STD can indeed cause lower back pain. The most common STD known to cause lower back pain is Chlamydia.
Simple testicular pain alone is rarely, if ever, an STD. An STD is an infection and if an infection gets down to your testicles, it infected everything along the path it took. If your penis and testicles hurt, an STD would become less unlikely. Pain while urinating or ejaculating might indicate an infection or STD. Lack of any symptom other than testicular pain makes STD pretty unlikely.