Jules I had 13 cysts drained, the specialist didn't bother with the other smaller ones, but due to the size and high number he suggested complete rest for a day or two, I also had a plane trip home, so he was concerned about that too. He also said they may have to be drained again if they refilled, but that hasn't been a problem. Only side effect was a slightly deeper voice and now not being able to sing in tune, due to them being wrapped around vocal chords.
Local GP had diagnosed terminal thyroid cancer with a prognosis of 6 months to live...if I was lucky!! That was early 1997, so (mentally) I was a bit of a mess, but fought on to get another opinion which was 'all clear, no signs of cancer', now who to believe with two totally opposite diagnosis. It seems the pathology lab got my tests/results mixed up with another patient who probably died unexpectedly due to having my results but all concerned went silent and nobody would discuss further.
For the last 18 yrs I've had CFS/ME brought on by another unrelated problem so it's difficult to say if the cysts had any impact, or not.
Not much help, but hope you get better support than I did. ;-)