I had a cyst on my ovary about 3 years ago. It grew bigger than a quarter, smaller than a half dollar. It got quite painful... My doc put me on progesterone based BC pills to try and shrink it--actually, it grew bigger. When it got about 3 cm in diameter, my doc removed it (larthoscopy, through the belly button).
Although there is no scientific evidence to support this opinion, I suspect that progesterone based BC pills brought it on. I had been on progesterone based BC pills soon after the birth of my daughter (while nursing) and that's when the cyst started; when I was on estrogen based BC pills (years before), I never had any cyst issues. When I was put back on progesterone based BC pills to shrink the cyst, it grew substantially bigger in those 2 months. Granted I was 36 at the time and cysts tend to occur as you grow older... however, I quit all BC hormones after the cyst/surgery. I'll be 39 in a few months and currently pregnant.
My advice is to deal with the cyst before you deal with more hormones and infertility. Get it removed if it doesn't resolve itself. Because you don't want it to grow around your ovary (and keep eggs from getting out) or attach to a blood vessel and starve the overy or eggs of blood and nutrients. Get off of the BC hormones and see if that stops the growth of cysts. Maybe your ovary will recover if the cycle of cysts is stopped? Then, after trying that, if the ovaries and cysts were not impacted by stopping BC hormones for a 8-12 months, then I would try the synthetic hormones and fertility drugs.
Good luck!