Did you already try putting extra breastmilk on it, quite a few times a day to see if that helped?
I don't know if the bite is near where milk would end up, but maybe if you put some on it more often than you feed it will help?
I'm not sure why the cut is green, but if it is fungal you would need an anti-fungal. Maybe if milk doesn't help try feeding off one side a few times in a row and put anti-fungal OTC stuff on it? I think a green cut could still be fungal, in which case antibiotics wouldn't help at all.