As kiamlaluno tells you, it is non-Standard to use good where an adverb is called for.
However, there's nothing wrong with using it with feel. Feel is ordinarily used as what grammarians call a copula: its complement is a quality attributed to the subject, and is therefore an adjective, not an adverb:
I feel pretty! Oh, so pretty! I feel pretty and witty and bright!
I feel really, really stupid.
I'm feeling pretty bad today.
And (again as kiamlaluno tells you) “I feel well” means you don't feel sick, but healthy.
If you use feel with an adverb you are probably employing it not as a copula but as verb of physical action. “I feel badly” means your tactile sense is impaired.