Yes, FOUGHT is a Scrabble word!

Letter values in Scrabble US: F 4, O 1, U 1, G 2, H 4, T 1.

Is it a valid word?

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

be engaged in a fight; carry on a fight
fight against or resist strongly
make a strenuous or labored effort
exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for

Also: fight back, fight down.