Yes, HIGHER is a Scrabble word!

Letter values in Scrabble US: H 4, I 1, G 2, H 4, E 1, R 1.

Is it a valid word?

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

advanced in complexity or elaboration
of education beyond the secondary level
greater than normal in degree or intensity or amount
(literal meaning) being at or having a relatively great or specific elevation or upward extension (sometimes used in combinations like `knee-high')
standing above others in quality or position
used of sounds and voices; high in pitch or frequency
happy and excited and energetic
(used of the smell of meat) smelling spoiled or tainted
slightly and pleasantly intoxicated from alcohol or a drug (especially marijuana)

Also: high-pitched, in high spirits.