Right lower pain is a concern. There are many important structures in this area which can cause pain. I would strongly recommend that you see your primary care doctor
in order to better evaluate this situation and subsequently treat it if required.
The right side of the abdomen, below the ribs, is classified medically as the right upper quadrant of the abdomen. The right upper quadrant contains many important structures. Most often, in otherwise your healthy people, it is actually not the insides that are causing the pain, but a part of the musculoskeletal system. Muscle or rib joint inflammation can cause this pain because of a sprain or strain.
However, there are many other important structures that can cause pain. The lungs (lower part of the right lung) can cause this is they are inflamed. A pneumonia
or a blood clot can cause this type of "pleurtic" pain (pain with deep breath. Other important structures are the stomach, liver or pancreas in the area. Inflammation of any of these can cause it. Most importantly, the gallbladder is here. What you describe would be consistent with gallstones.
This requires evaluation. Many of the above structures are vital and require attention. See your doctor.