Dragon Ella has it as well, her blocked tear duct became infected when she was a week old. She had antibiotics and the Peds said that the majority of blocked ducts will repair themselves over time. She still has it, I'm not surprised both my husband and I had ours unblocked surgically when we were babies.
The Peds recommended massage, saline and a cotton wool ball. Health Nurse recommended Breast Milk, it actually helps