Would spine or muscles be most likely to cause severe pain on right side of lower back?

It depends. Determining the cause of pain requires a thorough evaluation with a history and physical exam and possibly imaging studies and nerve tests.
Likely, Both. Could most likely be both. The spine can pinch nerves that would then cause the muscles to hurt or spasm resulting in your pain. If not resolved with conservative care and rest, see your doctor for further evaluation.

Related Questions

Severe pain lower back right side just above hip below ribs. (deep under muscle) no fever can't stand up straight. Most likely kidney or spine/nerve?

Let me explain. This location low for kidney problem beside if you have kidney problems you will have other symptoms. Also nerve injury usually follow certain pattern, if I have to educated guess most muscles inflammations. Read more...