I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you. It sounds like he has a meibomian cyst (or chelazion). These are not that uncommon in children and are caused by a blockage of the oil (meibomian) duct that leads from the gland to the edge of the eyelid where the oil is secreted to lubricate the eye. While they look infected they are actually like a pimple in that they contain oil, not pus, thus antibiotics are of no use in treating them. Most of these cysts will stop growing spontaneously and then can take many months to go back down. If it drains then you need not do anything as that will solve the problem and it will not come back. Don't try to squeeze or prick it as only the ophthalmologist can do that safely but they rarely drain them unless they have been present for a long time, usually more than a year, since other than the cosmetic appearance they cause no problem for the eye, vision, or the tissue around it.
Here is a reference on this condition that you might take a look at to see if that is what your son's looks like: http://www.irishhealth.com/article.html?con=197