As Ecossaise says, marked down is correctly used, but I'd find it more natural to say:
My essay was marked down because she thought what I wrote was incorrect.
Whatever is strange also: it implies everything. So it would have to be she thinks whatever I write, or she thought whatever I wrote. The whatever gives the sentence a general application - it suggests this always happens - which I wasn't sure you wanted. That is why I changed whatever to what.