We had this problems with DS2. Doc kept giving him the ab ointment to no effect, eventually I insisted on being referred to the eye department at the local hosp.
It turned out he had 'chalazion' prononced kuh-la-zion and not styes at all.
some info here
These are cysts that form on the eyelid and can be accompanied by blepharitis. Apparently no-one knows why some kids seem more susceptible to them than others, but they can tend to 'crop' which means you can get lumps appearing repetitvely on one or both eyes.
DS2 has blepharitis as well and we have to clean his lash margins with cooled boiled water and a tsp of bicarb morning and night to keep this under control.
DSs chalazions have never resolved with topical treatment alone. He has to have a course of oral antibiotics every time and now his consultant has told us to call the gp for a prescription as soon as a lump starts to appear. Annoyingly I can't seem to remember what the first ab he had was called, but it works within 3-4 days. Unfortunately after several recurrent episodes over the past 12 months the first ab started to be less effective and this last time he was given penecillin which shrank the lump within 48 hrs.
If it is chalazions, its important to keep up the warm compresses and at its worst this will need done around 4 times a day. (I know, its a right old pita.)
Its really important to get the right treatment as if the lump/s get too big and inflammed they can put pressure on the eyeball. (DS2 had one the size of one of those large marbles once, before we found out what the problem was, poor little thing couldn't see out of his eye.)