Thank you for the query.
rather gives upper right abdominal pain
radiating to the back with nausea and vomiting.
Lower right abdominal pain and back pain can be caused by urinary tract infection
or urinary tract stones. Frequent urinating and burning while urinating can be also present.
Lower right abdominal pain should be always checked with possible appendicitis
. With this condition nausea appears, the pain can aggravate while coughing or walking, heart rate is accelerated (above 100/min).
Other possible reasons of such pain are ovarian cyst
, ectopic pregnancy.
Abdominal CT is not a necessary test. More valuable can be urine analysis, blood work, CRP, pregnancy test and abdominal ultrasound.
Hope this will help.