It could be either one word or two words, depending on what you mean.
When it means yearning for your home, it is one word: I am homesick for Austria.
When it means staying home because you are ill, you could use two words:
Today I am home sick, but I'm going to work tomorrow.
one
iam homesick
There are two syllables. Home-sick.
I am homesick.
homesick, homeschool, homework, homemade, homeland, homelegence, homekeeper
It is two words. Writing it as one is acceptable in the UK and is referred to as a "Britishism." But in American grammar, it is always two separate words.
Subterranean Homesick Alien was created in 1997.
Homesick Heroes was created on 1988-08-15.
Homesick - The Vines song - was created in 2001.
Homesick James died on 2006-12-13.
Homesick James was born on 1914-05-03.
Homesick for St. Pauli was created in 1963.
Homesick - 2014 I was released on: USA: 2014