The first antibiotic known to modern medicine was an anti-syphilis drug called Salvarsan: https://en.wikipedia.org/wiki/Arsphenamine
The cream it would seem wouldn't be able to get to bacteria deepest into the cut.
Here's an example of E. coli developing resistance to a _strong_ antibiotic within 12 days [0].
Unfortunately, I know more than a few people who take antibiotics even when they get common cold/flu, which doesn't make sense since viruses are not bacteria and they should get vaccinated instead.
Allegedly almost all chickens have it.
It's not controversial that the two big drivers of this problem are the countries where antibiotics are available over-the-counter, and the widespread use of antibiotics in livestock.
These practices must end if we want to be able to keep using antibiotics to save lives in the future, and it is a question of policy alone.
On home medicines in general, though, I'd like to add a PSA. Put an annual event on your calendar to check your inventory to make sure you have an adequate supply and nothing is expiring soon.
It really sucks to say fall off your bike and somehow sprain your entire left side, making most movement agony, and then find that you need to go to the store because you are out of ibuprofen and acetaminophen.