Bad is always an adjective and should be used to describe a noun; badly is always an adverb and should be used to modify a verb. The adverb badly is often used inappropriately to describe a noun, especially following a linking verb.
Felt is a linking verb, so the adjective bad should be used to describe the noun sisters.
Exercises:
Adjectives and adverbs 1
Adjectives and adverbs 2
Adjectives and adverbs 3