"Sick" is ok as the context will make meaning clear. "Are you ill?" "Are you unwell?" "Are you not [very] well?" "Are you not feeling [very] well?" "Do you not feel well?" are all polite ways of asking the question, though there are many more ways of asking.
It is worth noting that in British English it is more common to use "ill" than "sick" and that "sick" is often used to mean vomit as either noun or verb.