Ah, this phrase is all about context. The meaning of “What’s up?” and expected responses depend on the circumstances in which the question is asked.

From what I remember, the phrase is derived from “What’s the update?” which is basically checking up how things are going. It has however fallen into common usage both in the US (I think) and UK.

As a greeting:

“What’s up?” or here (West Midlands of England) commonly just “sup” is a general greeting, you can response with answers like “Not much”, “Nothing”, “Alright” etc.

In this context, the response is just a return of the greeting, or a confirmation that all is going normally. This phrase is similar to “Hello” or “How are you” in common usage.

Example:

Person 1: “What’s up man?”

Person 2: “F*** all mate” (my typical response to friends, this means nothings going on and I’m bored because of it :^) )

As an enquiry

In this context, “What’s up?” can be when the asker of the question may have observed someone having some trouble, or is distressed at something.

It’s a polite, non-intrusive way of checking all is relatively okay or if they need assistance. A similar phrase would be “What’s the matter?” or “What’s the problem?”.

When facing criticism or disapproval of something, a common phrase is “What’s up with it?” meaning the asker is not sure what they have done wrong and wants to know what said issue is.

Example:

Person 1 notices Person 2 with their head in their hands at their desk

Person 1: “What’s up?”

Person 2: “Nothing, just tired.”

So to properly answer your question after rambling a bit. The idea behind “I am well” is sort of right – you are confirming that all is well and normal. So in this case “Nothing” or “Not much” or “Same Old” are all fine, and will be understood by a native speaker.

Personally, if I was speaking to a non-native English speaker and heard your response I wouldn’t think anything of it – it’s just a throwaway question so unless something really is up/wrong, the response is irrelevant.