Well is the "adverb form" of good, and good is an adjective. People in live speech mix these up all the time, though.
Adjectives can follow the verb to be, to feel, to seem, and a few other verbs, because these types of verbs take complements.
For example, you can say "I am hot" or "I feel sick." In these situations you can use good. You can also use well (e.g. "I am not well.") since a meaning of well when it is used as an adjective is "not sick."
Well as an adjective is not often used outside of a verb's complement. For example, it would be far more usual to say "I'm about the release all the patients that are well" than "I'm about to release all the well patients."
This contrived example might help illustrate also:
A: Did you test all the tools?
B: I did, each one is good. (You cannot say well here because tools are not a thing that get sick)
A: Well, give me one of those good tools. I need one. (Etc.)