I have to say this up front. I have no personal experience with sows. I have had boars for 15 years.
I will agree with you that doing nothing is not an option. From what you have stated here, I do believe that spaying is the best option, although I also understand your trepidation. The idea here is to look for as permanent a solution as possible, and the best one for Eri.
You are correct that the cyst may fill up again within days. This is also not optimal, and a recurrence even a week, month or year down the road isn't either. She is only 3, and potentially has a lot of life left in her.
Losing a pig during surgery isn't a given, but its also not out of the realm of possibility. The alternative is to either risk losing her (believe me, I don't take that lightly. I have lost several pigs over the last several years and I still grieve each and every one of them. I know that devastation)
OR risk having her in constant pain. In my opinion constant pain isn't an option, either. It isn't fair to her, or you or your daughter. If you were to lose her during surgery...... It could almost be seen as a blessing. I know how hard that sounds but after watching several pigs go through various different illnesses, it may be kinder that way.