Limburg cheese smells very (bad, badly).
Is the correct answer bad because it modifies cheese?
"The leading lady in the play," she said, "is feelin (sick, sickly)."
Is the correct anwer sickly because it modifies is feeling?
Your first answer is right because smells is used as a linking verb here.
Your second answer is wrong, because sick is a predicate adjective, following the linking verb, is feeling.
Study this site.
http://donnayoung.org/english/grammar/linking-verbs.htm