Hello and welcome to e health forum.
Abdominal muscle strains usually cause immediate pain in the area of the injured muscle. It can be hard to flex the muscle because of this pain. The other common symptom is muscle spasm of the injured muscle. Less commonly, swelling and bruising can result from the muscle injury.
In your case, a CT was ordered to rule out other conditions like renal stone or bowel conditions like appendicitis or rupture, which can also present as acute abdominal pain.
Though a CT can visualise intraabdominal organs, conditions associated with soft tissues like muscles (muscle tears) cannot be clearly differentiated, with a CT. Such conditions are better seen with a ultrasound or a MRI scan.
Hence I do agree with your doctors approach to managing your condition. You might continue with your doctors advice and treatment.
In case, you still have doubts, you can definitely seek a second opinion, to clear your doubts.