Everyone here has made very good hypotheses. Using the antibiotics for a short time when you began them could have caused the bacteria your chin may have to become resistant. I don't know how long it would take a bacteria like that to evolve that trait, though, but it seems plausible to me. If that's the case, your vet can prescribe you another antibiotic.
Antibiotics can be hit or miss. Some work, some don't. Sometimes several kinds are tried before one is effective enough to clear up the infection, like Stackie said.
These are all the causes I can think of for an eye infection:
Bacterial
Viral-your vet will most likely put her on antibiotics anyways along with whatever treatment for the virus is given to inhibit a secondary infection while her immune system works overtime.
Irritant- chemicals/toxins in environment for example, or a physical irritant like dust bath or injury. If both eyes are affected, then it's probably not something lodged in her eye or a scratch. If not, it may be worth looking into. Although infections usually start in one eye and may or may not travel to the other one, so it's not a sure sign.
Allergy
Maloclusion/Dental Disease- tooth root can grow into eye cavity and wound it, causing a subsequent infection. Ususally has other symptoms like drooling, pawing at mouth etc.
Fungus- I'm not sure there is a fungus that actually causes an eye infection, but ringworm often starts around eyes, nose etc and since it makes skin very dry a chin can itch their eye to scratch the infected skin around it and possibly injure the eyeball.
Other Illness- repiratory illness, colds etc can have watery eyes as a symptom with accompanying symptoms. I do not think the eyes are infected in these cases, though.
I would try using other antibiotics, strictly as prescribed and then talk to your vet about the other possibilities mentioned if it doesn't work. Watch out for other symptoms and if seen, visit your vet. Clean her cage thoroughly and try to isolate her since she might be contagious. Avoid giving her a dust bath right after you give her drops or eye medicine since the dust might stick around her eye and irritate it more.
