It is definitely best to consult an eye specialist to evaluate and assess the eyeball cyst. He will be the one to suggest treatment options and which is best for your condition. Depending on severity, surgery may be indicated.
I recommend going to the doctor. He'll most likely drain it for you. It doesn't hurt at all to have it drained and it only takes a couple of minutes. Although it may come back so it might take a couple trips to the doctor for it to go away permanently.
The cysts are usually due to collection of water(tears) in your conjunctivitis. They don't do any harm to your eyes. As its prevention you can do is to keep your eyes always clean. As cure cure you can do is the laser puncture. But if you have cyst you need not to worry.