Yes, FEELING is a Scrabble word!

Letter values in Scrabble US: F 4, E 1, E 1, L 1, I 1, N 1, G 2.

Is it a valid word?

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

the experiencing of affective and emotional states
a vague idea in which some confidence is placed
the general atmosphere of a place or situation and the effect that it has on people
a physical sensation that you experience
the sensation produced by pressure receptors in the skin
an intuitive understanding of something

undergo an emotional sensation or be in a particular state of mind
come to believe on the basis of emotion, intuitions, or indefinite grounds
perceive by a physical sensation, e.g., coming from the skin or muscles
be conscious of a physical, mental, or emotional state
have a feeling or perception about oneself in reaction to someone's behavior or attitude
undergo passive experience of:"We felt the effects of inflation"
be felt or perceived in a certain way
grope or feel in search of something
examine by touch
examine (a body part) by palpation
find by testing or cautious exploration
produce a certain impression
pass one's hands over the sexual organs of

Also: touch sensation, tactual sensation, tactile sensation, intuitive feeling.