There are a lot of sentences linked here in the vein of "I do not feel well". However, since there are so many clearer ways to express that feeling in English, I move to have all those sentences unlinked.

Native speakers: is this a good response to "How are you"?

Not for me.

"How are you?"
"Not good."* /"Not well."/"I'm not doing well."
*this is technically incorrect but it's used a lot (in America) to the point that no one cares

Either way, the least I would do is contract "I am" into "I'm" ( #9381512 )
Then that would mean something like "I'm not a good person"

@CK @AlanF_US
Thoughts?

People do say "I'm good" to mean either "I'm doing fine today" or "I'm doing fine at the moment and don't need any special attention":

"How are you these days?" "I'm good."
"Do you want any dessert?" "No, I'm good."

However, this is not really standard English. I agree that the primary meaning of "I'm good" in current usage is still "I'm a good person".

As for the negative, "not good", I can see it as a standalone answer to a question:

"How are you?" "Not good."

But I agree that "I am not good" sounds odd unless the speaker means that they're not a good person. I unlinked the sentences (in the languages I know) that did not have that meaning.

Thanks, @DJ_Saidez and @AlanF_US!

Thanks for raising the issue in the first place.