What could cause a large septated mass with unknown etiology to form on my right ovary? What questions should I ask my gyn?

Do we go in? My first and second choices would be endometriosis. The first question you need to ask your physician is, "do we go in and remove the mass for diagnostic / therapeutic purposes?".
Rapid growth. Rapid growth can cause rupture. The question you need to discuss is "what is it?" after that is answered, a plan can be developed. Second opinion is always an option. Remember, they work for you; you don't work for them!