Because I have impetigo on my arm, will neosporin work on it?

Impetigo. It may help but may not cure it. If there are only a few sores on the skin, a better antibiotic is Mupirocin (bactroban), more skin involvement usually needs an oral antibiotic. Please remember that impetigo is a very contagious disease that, if not treated correctly, may cause heart and kidney complications.