Doctors r/o inguinal hernia, diverticulitis, and testicular torsion. observed epididymitis. cause severe pain in ll abd. when sneezing/coughing?

Referred pain: The testicle and closely attached structures (epididymis) form in the abdomen very early in life and then migrate later to outside of the body. This means that the nerve supply originates in the abdominal area -and you are experiencing this firsthand. Hopefully the treatment for epididymitis will lead to resolution. Has anything been confirmed? Good to see doc to make sure you're on track to heal.

Strained muscle: Pain sounds musculoskeletal especially if it gets worse with straight leg raising. Could be muscle strain or radiculopathy. Given your age more likely the former. Try local heat but if no better an injection into the site of steroid can often help.