Welcome to the board! I know how scary it is to be told you have an ovarian cyst. The good news is that chances are very, very good that the cyst is benign and nothing to be worried about - especially given your age.
Most cysts resolve on their own - especially when they're as small as yours is.
It's pretty standard procedure for doctors to order follow-up tests with cysts to make sure that the cysts have gone away on their own.
Usually they'll order a follow-up ultrasound for 6 weeks after the original ultrasound. The thinking behind this is they want to see if the cyst persists beyond one menstrual cycle. If it goes away, it means that it was likely a functional cyst, and no further follow-up will be needed at this point.
If it's still there, then they might want to have further follow-up tests to monitor the cyst (ie: to keep tabs on whether it's growing, getting smaller, etc).
Even if it's still there when you get your follow-up ultrasound, please keep in mind that the vast majority of cysts are harmless.
You've mentioned that you're worried about your fertility - the cyst will likely not affect your fertility, but if you're worried about this you can ask about this when you go for your follow-up ultrasound (or if need be, you can book an appointment with the doctor who ordered the ultrasound tests).
Also, don't forget - even if for some reason your right ovary is affected permanently, you still have another ovary that also produces eggs, and I've read accounts of people who had to have one of their ovaries completely removed and were still able to get pregnant (with their remaining ovary).
So again, it's totally normal to feel worried, but chances are very good that everything's fine, and this is just a tiny blip on otherwise good health.
And there are lots of people on this board to give you moral support while you wait for your follow-up tests.