Aside from the linking-verb-action-verb trickiness, another reason people get confused about this topic is that well can be both an adverb and a predicate adjective. As I said earlier, in the sentence He swam well, well is an adverb that describes how he swam. But when you say, "I am well," you're using well as a predicate adjective. That's fine, but most sources say well is reserved to mean "healthy" when it's used in this way (1, 3, 4). So if you are recovering from a long illness and someone is inquiring about your health, it's appropriate to say, "I am well," but if you're just describing yourself on a generally good day and nobody's asking specifically about your health, a more appropriate response is, "I am good."