Primary peritoneal cancer is a very rare but very aggressive tumor of the lining of the abdominal cavity. There is still much that is unknown about this disease--pathologic examination of cells from several different kinds of tumors, including peritoneal cancer and certain kinds of ovarian cancer that start on surface of the ovaries, suggest that these diseases may actually be the same thing. Having your ovaries removed does make it very, very unlikely that you will ever develop ovarian cancer. However, in theory you could still develop primary peritoneal cancer because the disease can develop from any part of the lining of the abdominal cavity, not just from the surface of the ovaries.
Having ovaries removed in your 30's suggests that you may have a family history of ovarian/breast cancer. If you are concerned about other cancers, you should feel free to discuss these concerns with your primary care doctor
or the genetic counselors whom you hopefully talked to about cancer risk before your oophorectomy. Primary peritoneal cancer is quite rare, although it is more common in women who have the BRCA1/2 mutations that are the most common reason why women your age choose to have their ovaries removed. The best thing you can do if you know that you do carry this mutation is to continue to see your OB/GYN and primary care doctor as recommended for routine screening.