You can use either; everyone else does. So much so that I can't really judge which one is more natural. Traditional grammar says that only 'I feel good' is correct, but when an ailment looms, 'I don't feel well' is at least as common as 'I don't feel good' among native speakers.
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Mister MicawberTraditional grammar says that only 'I feel good' is correctDoes it? I didn't know that! Well is an adjective that has the following meanings according to Random House Unabridged Dictionary:
Mister MicawberMany people think that 'I feel well' only means 'I have sensitive fingers'.Right. This question has come up before, and I think opinion was divided. To me, "I feel well", meaning "I feel good", is fine: "well" is an adjective, no problem. However, I think, as you say, that some people understand it to mean that one's sense of touch is well deve