Yes, ANXIETY is a Scrabble word!

Letter values in Scrabble US: A 1, N 1, X 8, I 1, E 1, T 1, Y 4.

Is it a valid word?

ANXIETY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

(psychiatry) a relatively permanent state of worry and nervousness occurring in a variety of mental disorders, usually accompanied by compulsive behavior or attacks of panic
a vague unpleasant emotion that is experienced in anticipation of some (usually ill-defined) misfortune