Wound care is important but there are some common misconceptions regarding it. Use of peroxide is common but often done for too long. Peroxide is a free radical and is toxic to most cells. As such it is an excellent wound sterilizer and should be used right after a cut. However afterwards its continued use can be toxic to the very cells that close the wound and thus it will disrupt wound healing.
Use bacitracin, Neosporin or triple antibiotic ointment after the initial sterilization of the wound. Keep it loosely covered to prevent maceration (that puffy white skin that develops) and improve wound healing.