I'm having intense pain in my back on the right and lower side. I've been feeling nauseous and throwing up for the last 5 hours. What could this be?

Some possibilities. If one has very uncomfortable tummy pain, and is normally in good health, plus is not pregnant, the possibilities include: appendicitis (usually has fever), gall stones, kidney stone (very painful), constipation (crampy), stomach flu, etc... Most people with "intense pain", meaning much more than mild pain, need a doctor's evaluation to be sure it is not appendicitis, which would need surgery.
KIDNEY STONES CAN BE. How intense is the pain - kidney stones or any colic pain can do it Need to have evaluation and treatment. They can be treated but also may recur Occluded ureters could damage your kidney. .