Yes, it’s “correct”. But even complete nonsense can be written in a way that’s grammatically correct, so that’s sort-of the wrong question to ask. The real point is, does it sound natural? Would a native English-speaker say it that way?
The phrase “care for” is most commonly used to mean either (a) “look after” or (b) “be fond of” — neither of which fits your use of it. I’ve already suggested better ways of putting it.