It could very well be an ovary, and it can happen that only one ovary gets irritated. I read a document that said right side versus left side for double-organs like ovaries or kidneys depends on potassium and zinc deficiencies - quite fascinating!
If the pain is happening mid-way through your cycle, then it's Mitterschmertz, named for the German doctor who discovered that some women can experience discomfort during ovulation. I had lots of that type of discomfort when I was a kid.
If it's during your period then it's all that estrogen getting stirred up. Beware of any estrogenic foods such as tofu around this time and keep liver flushing. :)