Any pain should be a concern, that’s what pain if for, it’s your body’s warning system telling you that something is wrong. Abdominal pain can be a sign of many things ranging from serious to non serious. Typically the most serious problem it could be a sign of is an appendicitis (the appendix is on your right side), but it could also be an intestinal disorder such as Chron’s disease, colitis, or irritable bowel syndrome (IBS). Of course it could also be something simple like a pulled muscle.
That is happens only when you walk or stand could mean many things. When you sit down you are probably reliving pressure on the area that is problematic.
You should consult your doctor to be sure since there are some serious issues that abdominal pain can be a sign of.