Yes, HARSHER is a Scrabble word!

Letter values in Scrabble US: H 4, A 1, R 1, S 1, H 4, E 1, R 1.

Is it a valid word?

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

unpleasantly stern
disagreeable to the senses
of textures that are rough to the touch or substances consisting of relatively large particles
unkind or cruel or uncivil
severe
sharply disagreeable; rigorous