Of course it works. They're antibiotics, they're SUPPOSED to work against infections. The thing is, if people use them often enough, then the infections that are actually resist to antibiotics have a survival advantage and over time they become the *dominant* form of infection. Most infections, if you're young and of average constitution, wont kill you and will eventually be fought off by the body. But, if you're old or have a compromised immune system? Then you better ******** hope those antibiotics work fast enough. When your granny gets sick and dies of a throat infection that's resistant, you'll only have yourself to blame.
Doctors over-prescribe them because a) some doctors are lazy, b) some patients are whiny little shits that can't handle being sick for just a little bit longer even if it means society as a whole is healthier as a result, and c) they believe that some new wonder drug will come out to replace existing antibiotics that works just as well (fantasyland).