I've had ovarian cysts, and I know what it feels like. Will these same symptoms occur if I get one again?

They may or may not. Many women have ovarian cysts with no pain. Other cysts can cause pain. It depends on the type of cyst, its size, and whether there is any bleeding.
Possibly. If you have a new cyst it may or may not be the same. Some cysts are symptomatic while others are not. Some cysts may rupture and may cause more pain than usual. There can be a rare compliation of torsion of the ovary which can be very painful.