The underarm itch may possibly related to the scalp problem, though, because a condition called
seborrheic dermatitis (seborrhea, for short) can affect both. The cause is unknown--even infants get it--but it can cause itch in both the locations you mention. Perhaps the scalp was infected from scratching, but seborrhea itself is not infectious. Seborrhea can be controlled, but it comes back when it wants to, so you needn't hold that against your dermatologist.