Did they do an x-ray of her stomach and intestines? She could have blockage which is life-threatening!!!!!! My Mom had surgery at 86 years old for blockage... she's 94 now... Thanks to God who gave her more years....
Get appendix looked at possibly
it could be gall stones or ureteric stone,get her whole abdomen usg done,along with chest xray
The hospital shouldn't have discharged her with symptoms like that. You need to go back or get an emergency appointment with your doctor. The abdomen is tough, because sometimes pain refers to different areas, and there's a lot of different structures that could be having problems. An intestinal blockage can cause severe pain. Gastroenteritis can cause a burning sensation (been there, done that). There's the appendix. There's the liver, which is on the right side. There's the kidneys, gallbladder, small intestine, large intestine, pancreas, peritoneal membrane, etc., and they can all have problems. And the ends of the lungs come down there as well, as jemma said.
But yeah, kidney or gallbladder stones sound like a good place to start. Did they even do a physical exam? Sometimes ERs can be quite remiss when it comes to doing a full exam. They should be taking off clothing, listening to heart and lungs, looking in ears, and feeling the abdomen, as well as any other tests that might be warranted (like a neuro exam if you might have neuro problems). She probably does need an ultrasound, which could detect any stones, and probably a consult with nephrology and GI.
So yeah, you need to go see a doctor (again) now. If you go to the ER and they try to boot you, ask for the supervising attending. I think you can appeal discharges and they have to keep you until it's resolved (although I don't know if that applies to the ER).
A general doctor would be able to assess her condition and send her for an ultrasound and/or xrays and refer her to the right specialist.
She may have kidney stones, liver or gallbladder problem and with her painful breathing she may have something wrong with her lung like pleurisy.
Best wishes.