[David]

22 cents is double what it is in Houston but not unheard of on the East and West coasts. As others have written, a heat pump doesn't usually work much below freezing so it was running full blast and not providing much heating. Heat pump mini-splits are also sold with electric heating strips to help heating below freezing so check if it has them. In the future, some oil filled electric radiator type heaters would work better for less.

I'd check the math on how many watts the mini-split system is times the hours it probably ran over the billing period to determine if the bill seams possible. You could also read the meter, crank up the mini-split for a couple hours and then read the meter again to determine what the power draw is.