You know how everyone complains about antibiotic resistance? Yeah, they're not going to give some random antibiotic if they have no idea what something might be.
Modern medical ethics requires you always prioritise the individual over society, which means one should always give antibiotics if the benefits outweigh the downsides for this specific patient, even if that means you might cause antibiotic resistance for everyone else in the future.
Unfortunately not necessarily. For many chronic conditions an individual may very well develop an antibiotic resistant bug. There's even plenty on YouTube about standard penicillins and strep bacteria that start growing right inside the antibiotics. Look it up, it's fascinating.
You're assuming (and indeed US medicine seems to assume this everywhere) that since there don't usually seem to be major negative side effects from antibiotics they're harmless. However we are now confident they're not - lots of interesting things live inside us and whether or not they can cope with antibiotics varies, we're an ecosystem and so this intervention is a massive change to that ecosystem, and while it will usually be justifiable if we know there's an infection if we don't know that's now a gamble.
You don't get to complain about antibiotic resistance if at the first sign of an issue you demand a bathing in random antibiotics, especially if you don't even know if you have a bacterial infection in the first place
Antibiotic resistance could just as easily first happen in the sewers and other places where there is a lowish concentration of antibiotics.
The prisoner would undoubtedly have a better life if not imprisoned. But society does better if they are imprisoned.