I'm probably far from being an English expert, since English isn't even my first language, but the rules for adjectives and adverbs are pretty much the same in most European languages. An adjective describes how something is, an adverb describes how something is done. Adjectives describe objects (nouns), adverbs describe actions (verbs).
So to me the question would be: Is "good" a property of an object or of an action?
When you say "she looks good", good is an adjective and therefore must refer to "she". And that is probably exactly what you meant to say. You didn't mean to say that she performs a certain action in a good way, did you? As only then you'd need an adverb.
Now the confusion here probably stems from another fact, namely that "well" is the adverb of "good," as in "she's doing that pretty well" (here "well" actually refers to how she is "doing it", it describes a verb and is thus an adverb), but "well" is also an adjective in its own right; it is a synonym for "healthy."
So the statement "she looks well" is completely correct, but no one would see "well" as an adverb in this context, everyone would see it as an adjective, and so you just said "she looks healthy" which has a completely different meaning as before.