There is no oral antibiotic that will work on healing gangrene, wherever it is. Oral antibiotics do not kill the anaerobic clostridia that burrows into the skin and creates blisters filled with foul smelling pus and turns the surrounding skin green by killing the living cells of the skin and flesh.
Tell the doctor who prescribed the oral antibiotic for gangrene to go play golf!
Because clostridia is anaerobic, it fears oxygen. Soaking the infected toe in a bath of hydrogen peroxide will kill the clostridia and dry out the pus.
No oral antibiotic does that.