Final answer:
Ectopic pregnancy rupture is the most likely condition causing severe lower abdominal pain and radiating to the shoulders.
Step-by-step explanation:
The condition most likely to cause an adult female patient to present with non-traumatic lower abdominal quadrant pain reported as severe, agonizing, and often radiating to the patient's shoulders is ectopic pregnancy rupture. In an ectopic pregnancy, the fertilized egg implants outside the uterus, usually in the fallopian tube. When the fallopian tube ruptures, it can cause severe abdominal pain, which may radiate to the shoulders.