Yes, ALUM is a Scrabble word!

Letter values in Scrabble US: A 1, L 1, U 1, M 3.

Is it a valid word?

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

a white crystalline double sulfate of aluminum: the ammonium double sulfate of aluminum
a white crystalline double sulfate of aluminum: the potassium double sulfate of aluminum
a person who has received a degree from a school (high school or college or university)
a double sulphate of aluminum and potassium that is used as an astringent (among other things)

Also: ammonia alum, ammonium alum, potassium alum, potash alum.