Although it is possible to have ovarian cancer at a young age (I was 26 when I was diagnosed) having cysts does not mean you will get cancer. Many women have harmless ovarian cysts that never progress into anything...
Having cysts does not mean you will have cancer. It is a good idea however, to keep an eye on them because even harmless cysts can grow and cause other issues.
If you have concerns, you should definatley consult with your doctor about them...
I was diagnosed when I was 30, I was told then that the cancer had been growing for the better part of 10 years. If your concerned about it, you should take this up with your DR