Not sure if it's the same thing but I had a blocked gland on an upper eyelid which swelled up and eventually came to a head.
The way of getting rid of this was to apply warm compresses 3 times a day. Also, massage the eyelids, 3 times a day, from inner to outer edges, lightly using index or middle fingers.
It may be a different thing as my eye was very dry but the bag you mention sounds similar.