Bad is an adjective that modifies a noun. Adjectives follow linking verbs.
Badly is an adverb that modifies a verb. Adverbs modify action verbs.
If you say, “I feel bad,” you are using the word “bad” as as adjective meaning of poor quality. If you say, “I feel badly,” you are using the word “badly” as an adverb meaning in an unsuccessful way. In essence, you are saying that your fingers are not feeling things correctly.
Badly can also mean to a great or serious degree, so you could say, “I wanted a new car so badly” and it would be correct. So then, why is it not correct to say, “I feel badly,” because you are trying to imply to a serious degree?
The general rule is with most verbs it is correct to use the adverb “badly.” Linking verbs such as feel, smell, and am are the exception to the rule and in this case you would use “bad.” To determine if it is a linking verb or an action verb, replace the verb with “is.” If it still makes sense with the word “is,” it’s a linking verb. If not, it’s an action verb.
She feels bad.
She is bad.
(In this sentence “feels” is a linking verb because it still makes sense.)
She feels badly.
She is badly.
(In this sentence “feels” is an action verb because it no longer makes sense.)
A few other linking verbs are:
State of being — taste, look, appear, grow, seem and become.
Forms of to be — is, are, was, were, being and been.
Now you’re a little smarter, Girlfriend — And so am I.