What started as a tiny, harmless red speck on her eye developed into a fast-growing tumour behind her optic nerve.
By the time she was five weeks old, her left eye was so swollen that her mother Lynda, from Cumbernauld in North Lanarkshire, was constantly being accused of giving her baby a black eye.
The family's health visitor had to step in and advise social services that Georgia had a medical condition and was not at risk of abuse.
But after being one of the first in Scotland to be put on a trial drug to shrink the growth, which was close to attaching itself to her brain, Georgia is now a healthy three-year-old with perfect vision.
Normally the birthmark, called a haemangioma, grows on the skin. But in Gerogia's case it mainly grew internally - something that happens in just one in 100,000 cases.
Mrs Gibson, who was followed around the supermarket and had her car registration taken by concerned onlookers, said: "It was a nightmare. It started off as a little red spot on her eye and just got bigger and bigger.
"When she took a growth spurt it [the birthmark] got a big growth spurt too, because it feeds off the blood vessels. She just looked like she was being beaten up."
"Complete strangers would come up and ask, 'Did you hit your baby?, 'What's wrong with your baby's face, did you drop her?' You expect comments like that from kids, but from adults it was shocking. That's what I found the most hurtful."
Doctors told Mrs Gibson and her husband Richard that if Georgia's tumour had gone undiagnosed for another 10 days, it would have been untreatable.
Mr Gibson, a bus driver, now plans to walk 10 miles in aid of Yorkhill Children's Charity to thank the staff who saved their daughter and to help other children.
Mrs Gibson said: "We are so fortunate everything worked out and we had Yorkhill right on our doorstep."
The normal course of treatment would previously have been gruelling cancer treatment to shrink the benign growth. But following a chance discovery by a doctor in France, Georgia was given propranolol, a beta-blocker traditionally used to treat hypertension and heart conditions, which had been shown to shrink haemangiomas.
She has now made a full recovery. Her tumour is still there, but doctors have said it will continue to shrink and is no longer a threat.
Mrs Gibson said: "Now she has no mark on her at all and has equal vision in both eyes. She has been very lucky."
Anyone interested in taking part in the walk for Yorkhill should visit www.yorkhill.org/events/yorkhill-sponsored-walk