Hello
Pain in the right side abdomen ( lower part ) which radiating to the back may be due to these possibilities , these include:
1 Renal calculus , as this is a most common cause of such pain . Diagnosis can be confirmed by
ultrasound of abdomen ( both kidneys and whole of the
urinary tract system).
2 Amoebic colitis , as this is also a common cause of such pain , diagnosis can be confirmed by stool examination as well as physical examination by a physician because in amoebic colitis usually colon is palpable.
3 Urinary tract infection is another cause ,as you mentioned in the query . So get in urine culture for confirmation.
However, there are so many other causes of such pain on this side as epididmo-
orchitis ( if you are male ) , while if you are female then
fallopian tube infection may be the one such cause (
salpingitis ).
So in my opinion consult a physician and get his opinion as physical examination as well clinical and history of illness is important.
Good luck.