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It depends. It depends on who is asking the question and what he or she is asking about. If the question is specifically about your health then "I'm well" is probably the better response. If the question is about things in general then "I'm good" might be the better response.
The construction "I am xxx" is looking for an adjective.
When it comes to health, "well" (usually an adverb) is an adjective, meaning healthy. When it comes to other issues, such as general spirits, state of affairs, etc., "good" is quite acceptable.
It depends. It depends on who is asking the question and what he or she is asking about. If the question is specifically about your health then "I'm well" is probably the better response. If the question is about things in general then "I'm good" might be the better response.
Good vs. Well 
Linear Mode
