A early stye or chalazion wouldn't have formed a cyst or a bump yet. During this stage the affected area is quite tender to touch. Here is some information on treatment:
The most common cause for an isolated bump on the eyelid is a chalazion or a stye. These bumps form when a gland in your eyelid gets plugged up and possibly infected. It is very often associated with a condition called blepharitis.
The treatment for this condition, however, is not antibiotics but rather cleaning the eyelids with baby shampoo. Buy some unscented baby shampoo and, in the shower, but th shampoo on your index fingers. Close your eyes, and raise your eyelids (to get skin out of the way) and scrub back and forth along your EYELASH margin. This is where the gland openings are located. The warm water will soften the gunk in the plugged glands, the friction and pressure of your fingers will massage the glands, forcing the gunk out and the shampoo will wash it away. You can also use warm compress to the affected lids during the day as your schedule allows.
This treatment will help to treat the bump on your eyelid while at the same time solving your underlying blepharitis. The lump may take many weeks to go away but you should notice some improvement in a few days or so.
If she doesn't show some improvement by mid-week you may want to have her evaluated by an ophthalmologist
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