Okay so... the word bad is an adjective and should be used to modify nouns and pronouns. Badly, like most words ending in -ly, is an adverb and is used to modify verbs.

So why do we confuse them in speech so much? Mostly because of idiot assholes like me who for years wrongly encouraged an over correction - encouraging you to say badly when you were right about saying bad. I feel bad about that. There’s a special place in hell for me for correcting grammar in the first place and an even specialler place for being wrong when doing so.

Feel bad is the grammatically correct version when describing that you don't feel well physically or emotionally. "Feel," like all other sense verbs, can double as an action verb or a "linking verb.” Linking verbs such as to be and to feel can be used with adjectives because they describe a state rather than an action. Other linking verbs are sense verbs such as feel, seem, look, appear, smell, taste, and sound.

WRONG:

I want you so badly. (Actually, I’m very, very good at wanting you so bad.)

I feel badly I haven’t made you cum today. (My guilt issues make me very good at feeling bad about it.)

Your cum tastes badly. (Cum can’t taste, ding-dong.)

CORRECT:

I feel bad about cumming so quickly. (It’s okay sweetheart, you were just really, really excited.)

Your cum tastes bad. (Maybe less garlic tomorrow, okay hon?)

That welt looks bad. (I donno, it’s kind of hot.)

You suck badly. (No biting and please, try to act like you like it.)