Try not to worry! I know that is easier said than done, but cysts, especially smaller ones, are a pretty typical thing. They will probably just monitor it at that size to see if it resolves itself or grows. 4 cm isn't really too big, they dont usually look at removing until they are 7 or so, unless there is some big concern.
I'm sure you meant 4 cm, which really isn't that big. I wouldn't be too worried about losing an ovary over it. I had a 10x11 cm dermoid cyst, and they removed it the night I went to the ER because of the pain. I still have my ovary. So long as it's just one cyst and there are no signs of something like PCOS, I wouldn't worry about finding one on the left side. Cysts are formed when some part of ovulation goes wrong, so they're actually quite common. Depending on the type, you may simply be able to shrink it away with birth control.