Will clotrimazole and betamethasone cream treat a staph infection of the skin?

No: Clotrimazole fights fungus, not bacteria like staph. Betamethasone is a topical steroid, so it will make the area less red, but it does not fight bacteria causing redness. If you applied these, the symptoms might improve, but if it's a bacterial infection, the cause will remain and may worsen. Fortunately, healthy people's immune system can fight minor staph infections. If worse, see a doctor.