3.5cm is not that big and I didn't think there was much of a concern with ovarian torsion at that size. If the cyst ruptures, that can cause severe pain. That pain can linger for awhile. I assume you had a u/s when you went to the ER a month ago? Have you had one since showing the cyst is still there? Do you know if it's a simple cyst? If so, it seems it could be drained.
Not only is there risk of damaging ovarian reserve if you have surgery, there's risk of your ovary being removed. It happens far more often than it should because oophorectomy (ovary removal) is an easier and often more profitable surgery than cystectomy (cyst removal). So if you do end up having surgery make sure your consent form explicitly states that only the cyst can be removed and not the ovary or any other organs.
This website is helpful - http://ovaryresearch.com/ovarian_cysts.htm.
Are you trying to get pregnant right now?
When I was 19 I was diagnosed with a large 6 inch dermoid cyst on my right ovary.. My doctor told me I probably had it since birth and it just kept growing and growing.. since it was causing me a lot of pain He said they would definitely have to operate on me to remove it and there was a chance they could remove my ovary too.. The surgery wasn’t too painful, but doctor said he had to remove my right ovary and Fallopian tube because the cyst was so big that it twisted and damaged them.. The recovery wasn’t too bad but my biggest fear was not being able to have children, since I knew from a young age that I definitely wanted to be a mom.. Well that was 10 years ago.. I’m 30 and just had my first baby back in November.. So the answer is yes! You can have a baby after having an ovary removed! Your remaining ovary regulates and takes over ovulation.. What I would recommend is to take extra care of yourself...Eat nutritiously, exercise, take vitamins, don’t smoke or drink too much.. Basically treat your body like the temple that it is and do your best to protect your remaining ovary.. If you’re not trying to conceive go on birth control pills to “preserve” your eggs.. No need to ovulate if you’re not trying to get pregnant!! When you’re ready to get pregnant, get off of the birth control and give it a go!!! Might sound crazy but That’s what I did and now I have a beautiful baby boy.. He was conceived in my first month of trying, So YES you can have a baby with one ovary!!!! :)