I sleep under a blanket with the a/c on. i wake up with sweat from my right armpit through my light nightshirt. what's happening to me?

Don't know: I don't why you are preferentially sweating in 1 area of the body. Is there a difference in how your extremities are situated in relationship to cold stream of air? Is there is a difference in how blankets are covering 1 side vs. The other? Do you not this difference during hours when you are awake. Is the only area effected your arm pit? A dermatologist may be able to shed more light on this.

Sweat: If only your armpits get sweaty, then i would not worry too much. If you wake up in drenching sweats, then it may be a problem.