That appears to be a stye/chalazion.
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, put the 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 this doesn't work then the chalazion or stye can be removed with a straight forward surgery in your ophthalmologists office. Here is a good video that shows this procedure:
This takes care of this condition in the vast majority of cases.
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