I had an ovarian cyst about a year ago that resolved on its own. Do these cysts ever grow back?

Cysts will resolve. Small cysts on the ovary are very common even in young women. The overwhelming majority will resolve on their own without surgery. Although they may hurt the best treatment is to take Ibuprofen for the pain and to wait to see if it goes away. They don't grow back but you could certainly form a new one.