It is hard to know exactly what is going on without having some more information about where the cyst is located. However, I will assume that the area of swelling is in the eyelid at the edge of the lid, which is the most common place for this to occur. If this is in fact where the swelling is, then this is a stye or a chalazion, which are infections or blockages of the ducts that line the edge of the eyelid.
Usually these can be treated simply, with warm compresses and a bit of patience they will gradually go away. However, sometimes they can become a chronic problem. In this case, you may need to see your doctor
. Sometimes antibiotics are necessary in order to get the inflammation and infection under control.
In some rare cases, where the cyst grows and does not respond to antibiotics then a surgery
might be necessary to take care of the problem. This would be the last resort after trying more conservative approaches, including a long trial of antibiotics. If you are in this camp, then you should definitely set up an appointment with your eye doctor
to see what the next steps should be.