Is there a possibility of me having ovarian cancer if I'm only 20?

Yes. Ovarian cancer increases as you age, but even a 20 year old can have it, though very rarely.
Very unlikely. Unless there is strong family history and you have inherited a genetic defect related to ovarian cancer, a 20-year-old is not likely to have ovarian cancer. Possible, may be, likely, no.
Not likely. It is highly unlikely. Yet if you have anything abnormal bothering you dont hesitate to call your pcp to be seen.