Pain left side hip of lower back, no swelling or discoloration. Possibly from doing standing barbell twists. Is it possible and what to do?

Sprain/Strain. There are many potential causes of acute low back pain. The most common are sprain/strain injuries. Usually acute back pain will improve over 1-2 weeks with anti-inflammatories, gentle streching, and use of heat/ice. If your pain does not improve or gets worse you should contact your physician.