While it is possible that surgical intervention may be necessary for the treatment of your cyst; it is also possible that it will cause no further issue and will resolve on its own. It is good that your doctor is alerting you now of the possibilities, but considering that the possibility of a surgery during pregnancy in order to remove the cyst hasn’t been discussed, in all likelihood, the concern is not as large as you think it might be.
Obviously, any surgery on your reproductive organs (any abdominal surgery at all, really), is an absolute last resort measure during pregnancy. Really, due to the anesthesia, etc., any surgery at all is. And barring surgical removal, there’s not much to be done about your cyst. Depending on the cause/type of cyst, sometimes hormonal BC pills can cause fewer cysts to develop in the future, but again, not an appropriate course of action during pregnancy. With that said, if surgery is the best option, I'm very glad you've already had an answer from another woman who has had a positive outcome!
I had ovarian cysts on a few occasions before pregnancy (including one during a miscarriage that was already hemorrhaging and was allowed to bleed out on its own with no intervention – wasn’t even given pain meds although the pain levels were mind-numbing!), but never during pregnancy, and never in the 13 or so months between (to my knowledge). I used information from this site - http://www.earthclinic.com/CURES/ovarian_cysts.html
What I used and found beneficial were the beets, carrots, non-alcoholic wine and molasses. None of these are dangerous in pregnancy (actually, the beets and carrots are great!), although depending on your own feelings, you might want to steer clear of the non-alcoholic wine. There appears that there might be some “recipe” for amounts of these and a way to incorporate them together into some sort of “sludge” that is taken like a medicine, but I simply incorporated them into my normal diet and got results. Honestly, as I didn’t like the taste of the non-alcoholic wine since I wasn’t able to find a really good brand in my area, and only had a single choice of brand, I actually used very little and so I would say that the other ingredients were more beneficial. I do believe they helped me.
You’ll likely receive more ultrasounds during pregnancy than most women, simply to keep an eye on the growth of the cyst and positioning. It is possible you won’t, if they can determine what they need to know by palpating the cyst during exams if it is in an area where that is possible and won’t cause problems and based on your pregnancy weight gain vs. uterine growth.
I continued to measure a bit ahead of expectation during my previous pregnancy, and my midwife sent me for two ultrasounds to eliminate the possibility of cysts. With that being said, she indicated that she had assisted several women with natural, out-of-hospital births despite cysts, if the cyst was not in a position where the baby would be placed at risk. There are many possible outcomes, so no need to assume the worst-case scenario. I would simply relax, take what measures I can naturally to treat, and continue to follow the doctor’s recommendations regarding continued monitoring of the situation.