You are perfectly correct, although "well" can also be used as an adjective. "Good" is never an adverb though! The verbs "to feel", "to be" and "to become" are examples of linking verbs/verbs of incomplete predication, which take complements (these may be nouns or adjectives) rather than objects (which are nouns/pronouns). You can feel good or well (Remember "I feel pretty" from "West Side Story?) The problem here is the meaning of the word "good" which has moral connotations, whereas "well" has to do with health. It's complicated, and although I cringe when I ask somebody, " How are you?" and they reply, "I'm good," I fear that it's here to stay!