bandage up
To cover and/or treat one's wound(s). A noun, person's name, or pronoun can be used between "bandage" and "up." The trainer is bandaging Danny up right now—he should be back in the game soon. I bandaged up my daughter's knee after she fell at the park. As soon as we bandage it up you'll be good to go.
bandage someone or something up
to wrap bandages on someone or on someone's wounds. We should bandage the wounds up first. We should bandage up the wounds first. I have to bandage him up before we can move him. She bandaged herself up with the supplies she kept in her backpack.