Another ultrasound is needed to determine if it is there. Let's hope it has resolved itself. If not a laporascopic surgery may be needed. You don't need to worry if that is the case. It really is quite safe.
I understand your concerns, I have cysts on both ovaries and I am having surgery this Friday to remove them, I'm 44. I have had the problems for over a year now, well I got diagnosed with it over a year ago. To answer your question about size of the cysts 6cm is the size of a tennis ball, anything larger than 4cm the doctors usually consider surgery depending on how your pain is, what type of cysts it is your age and of course your current health. You really need to keep on top of this especially since the cysts had doubled in size. Try to express to your father the importance that you keep the follow-up appointment so your Gyno can monitor you properly. To see if the cysts are still there the doctor will do another pelvic ultrasound and possibly a vaginal ultrasound to get a better look.