Can your body defend itself against bacteria in a cut without antibiotics? I think it's awful to rely on antibiotics so much. So I am using polysporin (bacitracin and polymyxin)

Yes, of course... ...the body defends itself against infections in cuts, without antibiotics. Antibiotics have only been available for 75-80 years, but through the ages, most wounds didn't get seriously infected. Even now, antibiotics are not usually used to prevent infection in cuts; the main medical advice is to just keep the wound clean and dry. And FYI, polysporin (bacitracin and polymyxin) is an antibiotic ointment.