“I’m fine” has about twelve meanings. Pay attention to which one you’re hearing.

Two words doing that much work is a sign they are covering for something. Fine can mean genuinely fine, leave it, I do not want to cry here, I will tell you later, or I do not think you want the real answer. The word is identical every time. The pause before it, the face, and what happens next are what carry the meaning.

If it lands wrong, do not press. Say you are around later, then actually be around later. People tend to tell the truth eventually to whoever made it easy rather than to whoever asked hardest.