This is another case where the limitation of ASCII graphics leaves something to be desired. How big is the hole you just made? How much broken glass remains? Use your imagination, I guess; the game can’t really show you directly.
Clostridium tetani endospores can remain viable in situ for decades, and contrary to popular misconceptions, they can be found all over the environment, not just on rusty nails.
So raise your DEX stat higher next time. The game makes no assumptions about your character’s abilities unless it can derive them from your attributes and skills - no CDDA character is considered to be more dextrous than average unless their DEX attribute reflects that.
In the real world, antibiotics don’t ‘cure’ tetanus either. They’re used to treat the initial infection, but you need tetanus immune globulin to halt the effects of the tetanus toxin itself.
It’s not, even now. Break the window and then clean the broken glass out before climbing through.
This is how we test these things; without feedback like yours, we wouldn’t know if it’s happening too often or not often enough.