We are also solicitous about our aged/sick parents-in-law. is this sentence grammatically correct?

The use of a slash to join two words is not a grammatical item, it is an affectation used by people trying to seem more intelligent than they really are. What you wanted to say there is "aged and sick". Likewise, the use of dashes to join words. Omit the dashes.

"We are also solicitous about our aged and sick parents in law."