The normal meaning of "I am fine" in the UK is "I am well." If you are upset but don't want to talk about it, then you could say "I'm fine", but obviously your body language would betray your true feelings.

If someone says 'I'm fine' to me I take it at face value unless their body language or intonation reveals that something might be amiss. I would imagine people in the US do the same. I really struggle to believe the statement above, but hey, I hope someone from America chimes in and gives their opinion. 'I'm good' as an answer to 'how are you?' has become rather pervasive. Lots of people use it here too, although given you should use an adverb it's not strictly correct. But in informal greetings it's common. If someone asks someone how they are in the UK a very common answer is 'not bad' which always seems to confuse people not from this country. It's actually a positive thing. I normally say 'not (too) bad' or 'I'm OK/alright' unless I'm genuinely feeling really good that day.

"I am fine. Thank you." is used here in the U.S. to mean the person is....fine. The only time "I am fine" means trouble is when it comes from a wife to answer her husband's "How are you?". I shudder when I hear it.

In the UK, when we say 'I'm fine' it means exactly what it says. A person who answers the question 'How are you?' with the response 'I'm fine' is telling you that they are in good health and spirits. In fact, it is the standard positive response: How are you? I'm fine. How are you? Without any further context or background information, you have no reason to suspect that there's a problem or that they are covering something up. It simply means 'I'm well'. And to answer your additional question: Q: "Is it true that, if you're really feeling fine, it's not normal to answer 'I'm fine', but normal answers are 'I'm good' or 'I'm pretty good', or 'I'm great', or 'I'm all right'?" A: No, that's not true at all. If we are really feeling fine, we say 'I'm fine' or 'I'm very well'. Why shouldn't we? Fine means fine. 'I'm good' and 'I'm pretty good' are American-style answers that have taken hold in the UK over recent years, but they're mainly used by younger people. It doesn't seem natural to me to say either of those. For me, and for most GBE speakers of my generation, if a person is 'good' it refers to their skills or behaviour, not their state of health. 'I'm all right'. No. This is what we tend to say when we aren't fine. 'OK' and 'all right' are in the 'così così' range of responses. If we have been unwell or had any kind of misfortune, we say 'I'm all right'. When a colleague returns to work after an illness, well enough to work but not completely recovered, they'd respond to the inevitable "How are you's" with 'I'm all right'. Likewise a colleague returning to work after a bereavement would respond to your concern by saying 'I'm all right'. Obviously, they are not 'fine', but they are coping. They're not well, but they are all right. As Paul says, it would be interesting at this point to hear what some AE speakers have to add to this.

I can't vouch for young adults, but as far as I know, in the United States, "I'm fine" means "I'm fine." It's a very neutral answer. It's the expected answer to "how are you?" In my experience, in the US "I'm good" means "I don't need anything right now." For example, if a host is coming around with a coffeepot and asks "Do you want more coffee?" the traditional answer is "No, thank you," but a modern answer could be "No, I'm good." Tone of voice is everything. It is possible to say "I'm fine" in tone of voice that means you are expressing irony, you are not fine. "Yeah, sure, I'm fine, just fine, everything's ducky."