What is this ransid smelling lump behind ear?

outside cat came home with a lump behind ear with minor scrapes on it. now today it has a hole on the lump which has reduced in size and is pussie/lightly bloody and smells VERY ransid with white stuff (not pussie but fleshy almost) coming out of the hole????? bb? porcupine quill? cats nail poked a hole in the lump? fell and got a splinter??? do I pull out the white fleshy piece? leave it in there? just put peroxide on it and neosporine?