Is the following sentence acceptable?
Although I am always sick for my pet Chuck, I have to be happy and live.
Changing the context very subtly, what I could personally be happy with, as a NES, but not a teacher, would be something like:
"Although I am always homesick for my pet Chuck, I have to be happy and live [my own life] (e.g. when away from home/at college etc)."
In this type of situation, "for" would work for me.
homesick - definition of homesick by the Free Online Dictionary, Thesaurus and Encyclopedia.
Acutely longing for one's family or home - (AME)
Hope this helps