“Well” can be an adverb or an adjective. Or a verb. Or a noun. Or an interjection.
I’d agree that “I am well” would refer to one’s health. These days, “I’m good” seems to mean that the speaker is satisfied and needs nothing. It could also mean that the speaker is morally good, or skilled at something, but those seem less likely to me.
This could be wrong, but my German teacher (in University) once told us that when you say you’re “doing good” in English, this is incorrect. You should say you’re “well.” She said that the reason why English speakers say “I’m good” so often is a corruption that was contributed to in large part by native speakers of German. i.e., in German “gut” would be appropriate in many instances where “well” would be preferable in English.
I am not an expert, but if you told me, “I feel well,” I would think you were talking about your physical state: you feel the opposite of ill/sick. If you said, “I feel good,” I would think you were talking about your emotional state.
*“You just won the Boston Marathon! How do you feel?”
Gee, can’t anyone check a dictionary? “Well” can be used as an adjective, and the very first definition says “In a satisfactory condition; right or proper: All is well.”
When people say “I am well,” this is the one that’s meant. You can say “I am good” if responding to the question “Who here is a good tennis player?” If you’re talking about your condition, “well” is more correct.
I don’t think many native English speakers would interpret it that way. “I feel <adjective>” is fine as a construction (e.g. I feel sick. I feel weak. I feel unwell). “I feel good” = “I have a general feeling of wellbeing”.
If “well” were an adverb in “I feel well”, then that sentence would mean that I have a good tactile sense. Since it doesn’t, the only rational conclusion is that “well” is also an adjective. English is a Germanic language (although badly polluted by close contact with French over centuries) and Germanic languages, including older forms of English, do not clearly distinguish adjectives from adverbs. For example, the German word “gut” pretty much covers all the meanings of both “good” and “well”. So it is reasonable to suppose that “well” was originally an adjective that has mostly become an adverb, but is still used adjectivally in that one context.
Incidentally, the “-ly” suffix, now understood as an adverb former, originated as an adjective former and there are still a goodly number of adjectives that end in it.
Check a dictionary; “well” can be adverb or adjective according to context. In “I run well” it’s an adverb; but as Hari Seldon said, in “I feel well” it’s an adjective. Same construction as “I feel fit” or “I feel healthy”.
I worded it poorly, but what I was driving at was that “I feel good” does not mean “my sense of touch is acute”, and “I feel well” would mean that, as well as meaning “I am healthy”.
“I feel good” is technically incorrect in any situation, isn’t it?
At least from a mainstream UK English viewpoint, “I feel good” is correct, meaning only “I have a feeling of wellbeing” (as with James Brown). However, I gather from World Wide Words that there’s a minority view that it’s non-standard or over-colloquial, despite it’s use since the 19th century.
“I feel well” is also correct, meaning only the opposite of “I feel unwell”. Conceivably it could mean “my sense of touch is acute”, but for me that’d be a deliberately non-standard interpretation. As Grammar Court puts it, “I feel well” could be referring to your tactile abilities–just as “Time flies when you’re having fun” could be a command. The only thing is, it’s not.