If a cut is already infected, should i keep using neosporin?

It won't help: Neosporin may help preventing a small/superficial cut from infection, but once infected, epscially in deep wounds, it won't do much at all. The infected wound may need to be drained/cleansed and an oral antibiotic is likely needed. I would keep wound dry/clean and consult doc as soon as possible to minimize the wound from getting worse--infection may get to your blood stream(very bad). Good luck.