How To Confirm Infection In A Mole On The Head?

a relative has a mole on his head that is meaty and flesh colored. It has been there a long time. A few weeks ago , it grew much larger , he said like a small fish egg size. He lives in greece in a remote island and the medical world there is not that great. He has been to the dr. twice about this mole, he says it's also sore.; the first time they gave him a steroid injection with little effect, and this time they gave him a shot of an antibiotic. the dr. said it's infected. My question is , can a dr. usually look at the mole and give a diagnosis of infection, or does he absolutely need a biopsy. also if the swelling does start to come down with the abt, is that also verification that it indeed was an infection.