Given the data you provided (severe lower right abdominal pain sometimes related to urination and defecation, bouts of constipation pain), you might be experiencing gasses related to constipation. In constipation, the feces passage is slowed and the food decomposes further. This increases the amount of gasses in the bowels. The gasses might inflate the bowels, thus causing pain, if not released.


Constipation might be caused by an inadequate diet low in diet fibers that give the biggest part of the volume to the feces. Without them there simply is not enough feces to start the reflex of defecation. The pain might intensify during defecation or urination, because, in these cases, the abdominal pressure increases and more pressure is put on the bowels, too.


Bad eating habits, as well as stress might cause constipation. Pathological conditions in the anal area might cause pain during defecation. This might lead to reduced defecation and subsequently to constipation.


You might want to visit your family doctor for a physical examination and laboratory tests. You might be referred to a specialist for internal diseases (particularly eneterologist). Visual diagnostic methods (colonoscopy, for example) might be recommended to detect the cause of this condition.


The doctors might also want to rule out the presence of colitis (inflammation of the colon), which is usually presented with blood in the stool. The blood might only be spots, which you might have missed.
If only constipation is diagnosed, your doctor might recommend taking more food rich in dietary fibers. An enema might be recommended for regular defecation, which would also release the gasses.