Yes, GROWING is a Scrabble word!

Letter values in Scrabble US: G 2, R 1, O 1, W 4, I 1, N 1, G 2.

Is it a valid word?

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

(biology) the process of an individual organism growing organically; a purely biological unfolding of events involved in an organism changing gradually from a simple to a more complex level
(electronics) the production of (semiconductor) crystals by slow crystallization from the molten state

pass into a condition gradually, take on a specific property or attribute; become
become larger, greater, or bigger; expand or gain
increase in size by natural process
cause to grow or develop
develop and reach maturity; undergo maturation
come into existence; take on form or shape
cultivate by growing, often involving improvements by means of agricultural techniques
come to have or undergo a change of (physical features and attributes)
grow emotionally or mature
become attached by or as if by the process of growth

Also: spring up.