If the diagnosis is correct, that this is a viral conjunctivitis (what many people commonly refer to a pink-eye), and it sounds as though it is possible, if not likely on the basis of the history, then an antibiotic by its very nature will not affect or cure this. The reason for this is because antibiotics do not show any activity against viruses, only bacteria.
Viral conjunctivitis is most commonly caused by the same viruses that cause the common cold and so they most frequently follow having had a cold or a viral gastrointestinal illness, or they follow someone who has had fairly close contact with the same problem, as you have had with your wife. Because this does not respond to antibiotics, and because there is no specific anti-viral medicine that works against these viruses, unfortunately the virus just has to run its course. Usually, the virus runs its course through both eyes in about 1.5-2 weeks, without causing any permanent or long-lasting problems in the eyes, although occasionally the inflammation can be intense enough that it spills over from the conjunctiva to the cornea and causes an inflammation in the cornea that does not resolve on its own, but requires steroid drops to treat. This is uncommon, but possible.
It is a very common mis belief on the part of many persons, including primary care doctors and emergency room doctors, that taking antibiotic drops or pills for 24 hours will allow you to reach a non-contagious period in this illness and would allow you or children to go back to work or school without risking spread of the illness. As an ophthalmologist and eye surgeon, I can say with absolute certainty that this belief / dogma is false. Unfortunately, the virus is very contagious and if you were to touch your eye and then touch a table, let's say, and someone came along 12 days later and touched the same spot on the table and contacted their eye with it, they could also get the same illness. Generally, it is very difficult to abstain from work for 12 days, so the best advice I usually give is to abstain from work (if you work in a very customer-service oriented business, like handling money with customers, work in a grocery store or food-handling position, or work with many children or sick/elderly adults) until the eyes look and feel normal.
Until that time, cool compresses (cool works better to help the inflammation subside) and artificial tears 4-5x/day can help the eyes feel better.
It is also important to know the distinction between this viral conjunctivitis and a bacterial conjunctivitis. A viral conjunctivitis, as I said before, usually follows exposure to someone else with a similar red-eye illness and/or follows a cold or viral GI illness. It usually starts in one eye and then moves to the other eye within a few days, causes mattering/stickiness to the eyelashes in the morning and can cause burning, itching, light sensitivity and mild blurry vision during its course; but it usually does not produce copious amounts of thick, greenish discharge and the eye usually is not severely red or painful. If it is or if there is a lot of continual thick, greenish discharge and it is confined to one eye (for the most part), then this is more likely to be bacterial and should not only be treated with antibiotic drops, but should be evaluated by an ophthalmologist first to make sure it is not a severe, vision-threatening episode.
I know that's a lot of info, but the distinction between the two (viral and bacterial) is important to understand for the many reasons I discussed