If/When I am really hungry (literally- have great hunger)... (It's a fragment.)
The "am" can mean several different things depending on what follows (it can mean at, on, in, by, most, etc.). "Ich habe" means "I have."
Ich habe am translates as I have.....on...i.e.Ich habe am 5. November einen Zahnarzt-Termin - I have a dentist's appointment on November 5th.
Was habe ich heute gemacht? is German for What have I done today?
ich habe = I havenor is not a German word