So the best antibiotic in a SHTF for a long term is plain old stay clean and a bottle of hydrogen peroxide.
Good overall health and nutrition makes for a good immune system. We live in an incredible sea of microscopic organisms of all kinds, and 99.9% of them do us no harm. When we expose our good immune systems to all these organisms on a regular basis, we develop natural defenses and immunities against the few that are truly dangerous.
One of the sad things I've seen in my long career is how terribly sick and vulnerable children are who are kept too "clean" and everything they touch or eat is "sterilized." They usually don't have good nutrition or environment otherwise, and so never develop healthy immune systems.
So, "clean" is relative. Certainly keep wounds clean. But don't pour peroxide into them. Peroxide actually damages cells in a wound. If a wound is particularly dirty, flush with water that has been boiled with a little salt (1 tsp to a quart) and cooled. This will clean it, restore the natural saline balance, and not do any further tissue damage.
Peroxide can be very useful if there is sign of infection, however. Clean the wound as much as possible with the the salt water, then use a diluted solution of peroxide. Let it sit for a minute, then rinse it with the saline again.
Otherwise, good healthy dirt is your friend. Learn the difference between clean dirt (like good garden soil) and dirty dirt, such as found in a city gutter.